GEOMETRY CLASSWORK SPECIAL RIGHT TRIANGLES &
TRANSFORMATIONS
Special Right Triangles
Objective: Students will be able to
Find the remaining sides and angles given a side and angle of a right triangle,
Find the remaining side and the angles. given two sides of a right triangle,
In order to sharpen their knowledge for SAT
WARM UP:
The diagram shows the dimensions of a triangular city park. Does this city park have a
right angle? Explain.
1) A support wire for a telephone pole will be dropped from the top of the pole to the ground
at an angle of 45 0
How long must the wire be? Round your answer to the nearest tenth.
A. 6.9 m
*B. 11.3 m
C. 13.9 m
D. 16.0 m
1
2) Carl is preparing to clean out the gutters on his house. The gutters are 24 feet, 3 inches from
the ground. He plans to place the bottom of his ladder 6 feet away from the house and the
top of the ladder at the base of the gutter.
What is the length of the ladder that Carl needs? Round your answer to the nearest tenth.
A. 4.3 feet
B. 23.4 feet
*C. 25.0 feet
D. 30.4 feet
3) What is the value of x to the nearest tenth?
A. 4.2
B. 10.4
C. 13.0
*D. 13.4
4) What are the values for x and y in the figure below?
a) x  12, y  6 2
b) x  12, y  6 3
c) x  6 2 , y  6
d) x  6 3 , y  12
2
5) A student is making a model of a suspension bridge. A sketch of the model is shown below.
What length of wire should be cut to stretch from X to Y? Round your answer to the nearest tenth.
A. 30.0 cm
B. 38.7 cm
C. 41.2 cm
D. 50.0 cm
6) Patty is building a 6 feet by 8 feet rectangular platform as shown above. All corners form
angles. What is the length of the diagonal of the platform?
a) 14 feet
b)
28 feet
c) 10 feet
d) 14 feet
7) The city’s zoning department has regulations to determine clear vehicle sight lines—called
a Clear View Triangle—at all its intersections, as shown below
If m  F  90 0 ,
a)
75
ft
3
m, G  450 ,
b)
75
ft
2
and FG  75feet
c) 75 2 ft
d) 75 3 ft
3
8) Greg leaned his baseball bat against a wall after his game. The bat is 28 inches long and touches the
wall 20 inches above the ground, as shown in the figure below.
What is the distance, x, from the bottom of the wall to the point where Greg’s baseball bat touches the
ground? Round your answer to the nearest tenth of an inch.
A. 6.9 inches
* B. 19.6 inches
C. 27.6 inches
D. 34.4 inches
9) Dave has 17 meters of wire that he attaches to a lamppost 8 meters above its base, as shown below.
The other end of the wire will attach to a stake in the ground.
If Dave fully extends the wire from the lamppost to the stake, how far from the base of the lamppost
will the stake be? Round your answer to the nearest whole number.
A. 8 meters
B. 9 meters
* C. 15 meters
D. 19 meters
4
10) When the Sun is at an elevation of 45 0 , a tree casts a shadow 66 feet in length, as shown in the
figure below.
How tall is the tree?
a) 66 feet
b) 44 3 feet
c) 66 2 feet
d) 66 3 feet
11) Students in a geometry class are learning to use triangles to calculate distances. In the figure
below, the vertices J, M, and S represent the homes of Jason, Maurice, and Shanna, respectively.
How far does Jason live from Maurice, to the nearest tenth of a mile?
A. 6.0 miles
* B. 9.8 miles
C. 12.0 miles
D. 16.0 miles
5
12) The hypotenuse of a 30°-60°-90° triangle measures 10 inches. What is the area of the
triangle, rounded to the nearest hundredth?
A. 12.50 in 2
B. 17.68 in 2
* C. 21.65 in 2
D. 25.00 in 2
14) Starting from the same location, Paul walks 8 feet to the north, while Amy walks 12 feet to
the east.
What is the distance, h, between Paul and Amy, rounded to the nearest hundredth?
A. 9.79 ft
* B. 14.42 ft
C. 14.49 ft
D. 20.00 ft
13) Charlie has caught his kite in the top of a tree, as shown in the figure below.
He knows that the length of the kite’s string is 180 feet, and the angle the string makes with
the ground is 30 degrees. How far up the tree is his kite?
* A. 90 ft
B. 90 2 ft
C. 90 3 ft
D. 180 ft
6
14) A 12-foot tower is to be anchored by a wire running from the top of the tower to a point
5 feet from the bottom of the tower. What is the length of the wire?
A. 13 ft
B. 17 ft
C. 34 ft
D. 169 ft
15) Jeff lives on Oak Street, and Tom lives on Main Street
How much farther, to the nearest yard, is it for Tom to walk down Main Street and turn on Oak Street
to get to Jeff’s house than if he travels the shortest distance between the houses through an empty
field?
A. 46 yd
B. 48 yd
C. 126 yd
D. 172 yd
16) The side opposite the 60-degree angle of a 30°-60°-90° triangle has a length of 5 3 .
What are the lengths of the other two sides?
A. 5 3 and 5 3
B.
3 and 5 3
C. 5 3 and 10
D. 5 and 10
7
17 What is the value of x for the triangle below?
a) 2
b) 12 2
c) 12 3
d)24
18) A model rocket is launched. It rises to a point 36 feet above the ground, and is 48 feet along the
ground from the lift-off site, as shown below. What is the length of the rocket’s path in the air, to the
nearest foot?
A. 12 ft
B. 32 ft
C. 60 ft
D. 84 ft
19) Given ∆LMN below, ∠L is a right angle. Segment LN is 21 cm and MN is 28 cm.
What is the length of LM , to the nearest centimeter?
A. 7 cm
B. 19 cm
C. 35 cm
D. 49 cm
8
20) The graph above represents the floor of a new building. A straight electric cable will be
placed from A to C. What is the length of the electric cable to the nearest tenth unit?
A. 5.8 units
* B. 8.1 units
C. 13.5 units
D. 19.1 units
21) A 25-foot rescue ladder rests against a building. The base of the ladder is 7 feet away from the
building. How high can the ladder reach on the wall?
1
A. 12 feet
2
B. 16 feet
C. 18 feet
* D. 24 feet
22) A 6-foot man standing next to a flagpole casts an 8-foot shadow. At the same time,the flagpole casts
a shadow of 40 feet. Whatis the height of the flagpole? (Round to the nearest whole number.)
* A. 30 feet
B. 36 feet
C. 53 feet
D. 64 feet
9
Multiple Choice Test Taking Tips
Tips on answering multiple choice questions:
Read the question before you look at the answer.
Come up with the answer in your head before looking at the possible answers, this way
the choices given on the test won't throw you off or trick you.
Eliminate answers you know aren't right.
Read all the choices before choosing your answer.
If there is no guessing penalty, always take an educated guess and select an answer.
Don't keep on changing your answer, usually your first choice is the right one, unless you
misread the question.
In "All of the above" and "None of the above" choices, if you are certain one of the
statements is true don't choose "None of the above" or one of the statements are false don't
choose "All of the above".
In a question with an "All of the above" choice, if you see that at least two correct
statements, then "All of the above" is probably the answer. A positive choice is more likely to be true
than a negative one. Usually the correct answer is the choice with the most information.
Take and Retake:
The HSAs are given in October, January, May, and July/August. A special, seniors-only,
administration is given in April. Students can retake an HSA as many times as necessary to earn
either a passing score or a score high enough to allow them to use the Combined-Score Option .
Earning a combined score of 1208 on the three HSA tests (The Combined-Score Option allows
students to offset a lower score on one HSA test with higher score on another HSA test.);
http://www.montgomeryschoolsmd.org/schools/northwoodhs/HSA/strategies.html
http://hsaexam.org/
http://www.montgomeryschoolsmd.org/curriculum/hsa/
10
GEOMETRY TRANSFORMATION
objective: Students will be able to
- represent /draw and interpret the results of transformations and successive
transformations on figures in the coordinate plane.
•
translations
•
reflections
•
rotations (90°, 180°, clockwise and counterclockwise about the origin)
•
dilations (scale factor)
- identify locations, apply transformations, and describe relationships using coordinate geometry.
Compare transformations that preserve distance and angles to those that do not.
Solve problems involving transformations in order to solve real-world problem.
2
WARM UP: Use the matrices below to answer the question A  1
5
3
 1

0 , B  2
3
4 
0
1
4 
Which matrix represents the expression 2 B  A ?
 4
a)  2
 10
-6 
0 
- 8
 4
b) 3
1
- 3
2 
4 
 6
c) 2
 4
- 6
2 
0 
5
d) 0
7
6
- 1
4 
11
Definition:
Reflection over a line k (notation rk) is a transformation
in which each point of the original figure (pre-image) has
an image that is the same distance from the line of reflection
as the original point but is on the opposite side of the line.
Remember that a reflection is a flip. Under a reflection, the
figure does not change size. rk ABC   A' B' C '
The line of reflection is the perpendicular bisector of the
segment joining every point and its image.
A line reflection creates a figure that is congruent to the original figure and is called
an isometry (a transformation that preserves length). Since naming (lettering) the figure in a
reflection requires changing the order of the letters (such as from clockwise to
counterclockwise), a reflection is more specifically called a non-direct or opposite isometry.
Properties preserved (invariant) under a line reflection:
1. distance (lengths of segments are the same)
2. angle measures (remain the same)
3. parallelism (parallel lines remain parallel)
4. colinearity (points stay on the same lines)
5. midpoint (midpoints remain the same in each figure)
6. orientation (lettering order NOT preserved. Order is reversed.)
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Reflecting over the x-axis: (the x-axis as the line of reflection)
When you reflect a point across the x-axis, the x-coordinate remains the same,but the y-coordinate is
transformed into its opposite.
The reflection of point x, y  across the x-axis is point x, y  . M x, y   rxaxis x, y   M ' x, y 
Hint: If you forget the rules for reflections when graphing, simply fold your graph paper along the line of
reflection (in this example the x-axis) to see where your new figure will be located. Or you can measure how
far your points are away from the line of reflection to locate your new image. Such processes will allow you
to see what is happening to the coordinates and help you remember the rule.
Reflecting over
y  k : (parallel to x-axis)
When you reflect a point across y  k , the x-coordinate remains the same,but the y-coordinate is
transformed into 2k-y.
The reflection of point x, y  across the x-axis is point x,2k  y  . M x, y   rx axis x, y   M ' x,2k  y 
13
Reflecting over the y-axis: (the y-axis as the line of reflection)
When you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is
transformed into its opposite. The reflection of point x, y  across the y-axis is point  x, y  .
M x, y   ry axis x, y   M '  x, y 
Reflecting over the
x  k : (parallel to the y-axis )
When you reflect a point across x  k , the y-coordinate remains the same, but the x-coordinate is
transformed into 2k  y . The reflection of point x, y  across the y-axis is point
2k  x, y  . M x, y   ry axis x, y   M ' 2k  x, y 
Reflecting thru the origin also call 180 degree rotation
When you reflect a point across the origin, the y-coordinate is transformed into its opposite , and the xcoordinate is transformed into its opposite. basically, just change signs. The reflection of point x, y  across
the origin is point  x, y  . M x, y   rorigin x, y   M '  x, y 
Reflecting thru a different point
The reflection of point x, y  across a point h, k  is point 2h  x,2k  y .
M x, y   rh.k  x, y   M ' 2h  x,2k  y 
14
Reflecting over the line y = x or y = -x:
(the lines y = x or y = -x as the lines of reflection)
When you reflect a point across the line y = x, the x-coordinate and the y-coordinate change places. When
you reflect a point across the line y = -x, the x-coordinate and the y-coordinate change places and are negated
(the signs are changed).
M x, y   ry  x x, y   M '  y, x 
The reflection of the point x, y  across the line y  x is the
point  y, x .
The reflection of the point x, y  across the line y   x is the
point  y, x .
M x, y   ry  x x, y   M '  y, x 
Reflecting over any line:
Each point of a reflected image is the same distance from the line of reflection as the
corresponding point of the original figure. In other words, the line of reflection lies directly in
the middle between the figure and its image -- it is the perpendicular bisector of the segment
joining any point to its image. Keep this idea in mind when working with lines of reflections
that are neither the x-axis nor the y-axis.
Each point of the original figure and its image are the same distance away from the line of reflection (which
can be easily counted in this diagram since the line of reflection is vertical).
15
90 degree rotation
Flip order of x and y. Change signs according to what quadrant it's in.
ROTATION ABOUT A POINT WHICH IS NOT THE ORIGIN
Rotation is the transformation along circular paths. Rotation angle  dtermines the amount of rotation for
each vertex.
- sin  
cos 
In order to rotate a point around the origin you use the rotation matrix 
cos 
sin 
Let M x, y  be any point on the plane.
Then the rotation of the point M about an angle  about the origin maps it onto a point M ' x' , y' such that
- sin    x 
 x'  cos 
which is the rotation of the matrix about the origin through an angle  .

 y ' sin 
cos   y 
  
To rotate about a point that is not the origin, first you move all the points so the center is the origin, use the
usual rotation matrix, and then move all the points back to where you found them.
For instance, if the center is (3,5) you first subtract (3,5) from all the coordinates, then use your matrix, then
add the (3,5) back to
everything.


Example: If M 10, 3 is rotated about an angle 30 0 , determine the image point.
here   30 0 , Cos30 0  
cos 30
sin 30

3
1
, Sin 30 0   . Rotation matrix is given by
2
2
 3
1
- 

- sin 30
2
 2

cos30   1
3


2 
2
Substituting the above values
 3
 x'   2
 y '  
  1

2
1
-  10
2     4.5 3 

  
7 
3   3  

2 
Therefore, the image point is given by M ' 4.5 3 ,7 
16
INDEPENDENT PRACTICE
Graph the image of the figure using the transformation given
1) reflection across the x-axis
2) reflection across y = 3
reflection across y = 1
reflection across the x-axis
17
reflection across the x-axis
reflection across y = −2
T(2, 2), C(2, 5), Z(5, 4), F(5, 0)
H(−1, −5), M(−1, −4), B(1, −2), C(3, −3)
Write a rule to describe each transformation
18
Draw the image according to the rule and identify the type of transformation
x, y   x, y
x, y   x  2, y  5
x, y  2  x, y 
x, y    x, y 
x, y   x, y 
x, y    1 x, 1 y 
2
2 
Complete the ordered pair rule that transforms each triangle to its image. Identify the transformation.
Find all missing coordinates.
19
BCR: An air traffic control system at Little Rock National (LIT) airport, located at (2, 3) on the grid below,
uses a radar system that sends out signals to determine the locations of airplanes. This system can detect
planes within a circular region having a radius of 35 miles from LIT. Each grid unit represents 5 miles.
An airplane is heading directly toward LIT from the location represented by coordinates  4,7 on the grid.
1. Can the plane be detected by the radar? Support your answer with mathematical evidence.
2. The air traffic controller instructs the pilot to begin circling the airport halfway between the airport
and her current location. What will be the coordinates of the plane’s location when the pilot begins
to circle the airport? Show your work or explain your answer.
20
MULTIPLE CHOICES
1) RST is shown below
If RST is rotated clockwise about the origin, what will be the coordinates of the image of point T?
A) 6,2
b)  6,2


0
 x'  cos  180

 y ' 
0
  sin  180




c) 6,2


- sin - 180 0  6
 x'   1




 y '  0
cos - 180 0  2
  
*d)  6,2
0  6 
 x'   6 
  



- 1 2
 y '  2
21
2) Use the graph below to answer question
Which graph shows a reflection across the x-axis of the image above?
a)
b)
22
3) The figure below is rotated 90 0 clockwise about the origin, then reflected across the y-axis.
What is the final figure?
23
4) Josh is designing a cover for a paperback book. He is going to use the graphic shown above. He plans to
reflect the graphic over the y-axis. What will be the coordinates of the reflection of point A?
a)  5,8
*b) 5,8
c) 5,8
d) 8,5
5) Roberto is a computer graphics designer and is working on an ad for the local coffee shop. The figure
above shows a coffee mug in two different positions. Which describes the transformation of the coffee mug
in position I to the image in position II?
A. a reflection over a horizontal line and a translation down
* B. translation down and a reflection over a vertical line
D. translation to the right and a reflection over a vertical line
C. 180° rotation
24
6) The figure graphed below is rotated 90 0 clockwise about the origin and translated up 1 unit.
Which is the resulting image?
a)
b)
c)
d)
25
7) Which image will result from the figure below being rotated 90q clockwise about the origin and then
reflected across the y-axis?
a)
b)
26
8) Polygon STUVW is shown below.
After polygon STUVW is reflected across the y-axis, what are the coordinates of S′, the image of point S
after the transformation?
A. (−5, −2)
B. (−5, 2)
* C. (5, −2)
D. (5, 2)
9) The figure below is translated 3 units to the right, then 5 units down, and finally reflected over the x-axis.
What are the coordinates of the image of point X after the transformations?
A. (−2, −2)
B. (−2, 2)
C. (2, −2)
D. (2, 2)
27
10) RST is shown below.
If RST is rotated 180 0 clockwise about the origin, what will be the coordinates of the
image of point T?
a) 6,2
b)  6,2
c) 6,2
d)  6,2
11) If the parallelogram below were translated 3 units left and 6 units down, what would be
the coordinates of the new image W′X′Y′Z′?
A. W′(–2, –1), X′(0, 3), Y′(5, 3), Z′(3, –1)
C. W′(4, –1), X′(6, 3), Y′(11, 3), Z′(9, –1)
B. W′(–1, –2), X′(3, 0), Y′(3, 5), Z′(–1, 3)
D. W′(7, 8), X′(9, 12), Y′(14, 12), Z′(12, 8)
28
12) Triangle JKL is translated 4 units left and 5 units up. What are the coordinates of the
image of point J?
A. (2, 6)
B. (3, –3)
* C. (– 6, 6)
D. (–2, 6)
13) What would the figure below look like if it were reflected over the x-axis?
a)
b)
c)
d)
29
14) Triangle QRS is shown in the graph below.
Which of the following graphs shows ∆QRS rotated 90 degrees counterclockwise about the origin?
a)
b)
c)
d)
30
15) Segment JK JK is reflected across the y-axis to form J ' K ' . What are the coordinates of J′ and K′
A. J′(– 4, –5), K′(–2, 1)
B. J′(5, – 4), K′(–1, 2)
C. J′(4, 5), K′(–2, 1)
* D. J′(5, 4), K′(1, –2)
16) The arrow above represents the needle on a compass. The needle is rotated 180° in the clockwise
direction. What are the coordinates of point A after the rotation?
A. (–8, –6)
B. (–8, 6)
* C. (–6, –8)
D. (6, –8)
31
17) Triangle PQR has vertices of P(–2, –1), Q(1, 6), and R(3, –2). What are the coordinates of the vertices of
the image of ∆PQR if the figure is translated 4 units right and 3 units up?
A. P′(2, 2), Q′(5, 9), R′(7, 1)
B. P′(1, 3), Q′(4, 10), R′(0, 2)
C. P′(– 6, 2), Q′(–3, 9), R′(–1, 1)
D. P′(– 8, –3), Q′(4, 18), R′(12, – 6)
18) The point of the heart (H) has a coordinate of (–5, –7) as shown above. The heart is reflected over the yaxis and then reflected over the x-axis. After both reflections, what are the coordinates of the point H?
A. (–5, –7)
B. (–5, 7)
C. (5, –7)
* D. (5, 7)
32
19) The polygon above is the mapping of a school building. What translation rule moves point A
to the point (0, 0)?
A. x, y   x  4, y  2 B. x, y   x  2, y  4 C. x, y   x  4, y  2 D. x, y   x  0, y  0
20) Which transformation describes the change from Figure M to Figure N?
A. dilation
* B. reflection
C. rotation
D. translation
33
21) Sacha planned a fabric design by reflecting the triangle shown above over the x-axis. Which
list of coordinates represents the vertices of the triangle reflected over the x-axis?
A. (–2, –3), (–4, –6), (–8, 1)
C. (2, –3), (4, –6), (8, –1)
B. (–2, 3) , (–4, 6), (–8, 1)
D. (3, 2), (6, 4), (1, 8)
22) Which would move Flag A to Flag B in the graph below?
*A. clockwise rotation of 180°
B. reflection over x-axis, then clockwise rotation of 90°
C. translation 8 units left and 7 units down
D. reflection over y-axis, then translation 8 units left and 7 units down
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23) To plan a scene in an animated movie, Roger rotates the below figure around point P by 90° in a
clockwise direction. Which drawing shows the pre-image and the final image?
a)
b)
c)
d)
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24) A quilt design is formed by translating a polygon across the coordinate plane as shown in the figure
below. Which is a translational rule that will translate point A to point B?
A. x, y   x  0, y  8
B. x, y   x  4, y  2 C. x, y   x  2, y  3 * D. x, y   x  4, y  2
25) After this translation x, y   x  3, y  2 of point T, what are the coordinates of the new point?
A. (–1, 3)
B. (0, 4)
C. (3, –2)
D. (5, –1)
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26) Janelle and Franz are playing a game. The rule of the game is each playing piece must go through
one transformation. Janelle reflects piece X over line 3. Where will piece X land?
A. on piece A
* B. on piece B
C. on piece C
D. on piece D
27) Which graph represents the figure below reflected across the y-axis?
a)
b)
c)
d)
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28) The coordinates of C are (--4, 1). Which translation moves ABC to A' B' C' ?
A. translate 8 units left, 4 units up
C. translate 3 units right, 8 units down
B. translate 3 units left, 8 units up
* D. translate 8 units right, 4 units down
29) The point on the grid is reflected across the y-axis. What are its new coordinates?
A. (--5, 2)
B. (--2, 5)
C. (2, --5)
D. (2, 5)
30) After translating the point (x, y) four units to the right, what are its new coordinates?
A. x, y  4
B. x, y  4
C. x  4, y 
D. x  4, y 
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31) Which figure represents a rotation of figure 1?
A. figure 2
* B. figure 3
C. figure 4
D. figure 5
32) What are the coordinates of PQRS after a translation of 6 units to the right and 6 units up?
a) P0,3 , Q3,3 , R3,3, S 0,3
c) P0,3 , Q3,3 , R3,0 , S 0,0
b) P 6,3 , Q 3,3 , R 3,0 , S  6,0
d) P 3,0 , Q0,0 , R0,3 , S  3,3
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33)Triangle ABC is reflected over the x-axis. What will be the coordinates of A', B', and C'?
a) A'  1,1 , B' 1,3 , C ' 2,1
A' 2,1 , B' 1,3 , C'  2,1
b) A' 2,1 , B' 1,3 , C '  2,1 c)
d) A' 1,3 , B' 2,1 , C'  2,1
34) Which shadow shows a reflection of the corresponding figure?
a)
b)
*c)
d)
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35)Which of the following figures represents a 270 0 clockwise rotation of the flag about point A?
b)
a)
c)
d)
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36) Which is a reflection of the below figure across the x-axis?
a)
c)
b)
d)
42
37)
B'?
a) b) *c) d)
AB is translated 3 units left and 1 unit down to form A' B' . What are the coordinates of A' and
a) A'  4,1 , B' 2,0
b) A'  4,2 , B' 2,0
c) A' 1,2 , B' 0,2
d) A' 2,2 , B' 0,2
38) If point P has coordinates  3,7 as shown on the grid below, what are the coordinates of the point
P', the reflection of P across the x-axis?
a) 3,7 
b)  3,7
c) 3,7
d)  3,7
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39) Which of the choices is a reflection over the y-axis of the triangle shown below ?
b)
a)
c)
d)
The image of the point (4,-3) under a reflection across the x-axis is
(-4,-3).
a) true
b) false
40)
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41) The image of the point (-5,4) under a reflection across the y-axis is
(5,4).
a) true
b) false
42) The image of the point (-1, 8) under a reflection across the line y =
x is (8,-1).
a) true
b) false
43) This graph illustrates a reflection over the x-axis.
a) true
b) false
44) This graph illustrates a reflection over the x-axis.
a) true
b) false
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45) BCR:
Triangle ABC has coordinates A(-3,3), B(3,2) and C(-1,-4). If the
triangle is reflected over they-axis, what are the coordinates of image
triangle A'B'C'?
46)
The line of reflection between these two triangles is y = -1.
a) true
b) false
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47) BCR: a.
Which point is a reflection of point A over the x-axis?
b. Which point is a reflection of point A over the y-axis?
c. Which point is a reflection of point A over the line y = x?
This L-shaped figure is reflected over the y-axis. The image is
then reflected over the x-axis. What are the coordinates of the vertices
of the final image?
48)BCR
47
Which of the following descriptions (pertaining to the graph at the
right) is true?
49)
a) A" B"C" is a translation of ABC
c) ) A" B"C" is a reflection in the origin of ABC
b) A" B"C" is a glide reflection of ABC
d) A" B"C" is a dilation scale factor 2 of ABC
Which of the following transformations is illustrated by the graph at
the right?
50)
dilation
b) reflection in y = x
d) reflection in the origin
a)
c) translation
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51) Which of the following descriptions does NOT pertain to the
transformation shown at the right?
a) translation of vector  7,3
b) x, y   x  7, y  3
c) 7 units down and 3 units left.
An isometry is a transformation of the plane that preserves length.
a) true
b) false
53) If a reflection in the line y = -x occurs, then the rule for this
reflection is:
52)
a) x, y   x, y 
b) x, y    x, y 
c) x, y    y, x 
d) x, y    y, x
54) BCR: Angle
ABC has been reflected in the x-axis to create
angle A'B'C'. Prove that angle measure is preserved under a reflection.
Answer
Let's see if this is true using slopes.
Since these slopes are negative reciprocals, these segments are perpendicular, meaningm<ABC =
90º.
,
. Since these slopes are
negative reciprocals, these segments are perpendicular, meaningm<A'B'C' = 90º. Angle measure
is preserved.
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http://www.regentsprep.org/Regents/math/geometry/MultipleChoiceReviewG/Transformations.htm
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