Mastery Learning Algebra 1
Parallel/Perpendicular Lines, Distance/Midpoint
Parallel Lines SAME SLOPE
1.
1. A highway is being built parallel to the train tracks.
The equation of the line for the tracks is 3x  7y  11 ,
what is the slope of the highway?
A. 3/7 B. 7/3 C. -3/7 D. -7/3
2.
2. The equation of a line containing
one side of a

parallelogram is 2x  5y  8 . The opposite side
contains the point (5, -4). What is the equation of the
line that contains the opposite side?
A. y = 2/5 x – 6 B. y = -2/5 x – 4
C. y =
-2/5 x – 2 D. y = 2/5x – 3
Perpendicular Lines OPPOSITE RECIPROCAL
(change the sign and flip the fraction)

Ex: -5 
1
5
Ex:
3
 4
4
3
To find slope the equation must be in slope
intercept form y  mx  b (solve for y)
 = 9
Ex: Find slope of 7x – 3y

 -3y = -7x + 9 (subtract 7x)
y = 7/3 x – 3 (divide by -3)
Slope is 7/3.
Slope of parallel is 7/3
Slope of perpendicular is -3/7
Use given information (read the questions
carefully!): Look at the answer choices because
some can be eliminated if slope is not the same
(parallel) or opposite reciprocal. Then graph
the answer choices, look at the table and look
for the point it goes through or the y-intercept.
3. Line m is parallel to line n and passes through (5, -7). If
the equation of n is y=-3/5x + 2, which describes
m?
A. line m has a slope of -3/5 and a y-intercept of -4
B. line m has a slope of -3/5 and a y-intercept of -7
C. line m has a slope of -3/5 and a y-intercept of 2
D. line m has a slope of 5/3 and a y-intercept of -4
4.
Which is an equation of a line parallel to
y
Special Cases
Vertical lines have a slope that is undefined
Ex: x=3
Horizontal lines have zero slope
Ex: y=-2
Changing Variables in an equation:
1. Plug in correct numbers for the
variables
2. Graph the equation
3. Change the number(s).
4. Then look at the new graph.
Ex: Consider the equation y = mx + b in which m
< 0 and b > 0. What happens to the x-intercept
if b increases and m remains the same?
So let m be -2 and b be 4.
The graph crosses the x-axis at 2.
Now increase b to be 6 and keep m at -2
The graph now crosses the x-axis at 3
The answer is: x-intercept increases
2
1
–2
–1
–1
1
2
x
–2
A. y = 2x + 3
B. y = -2x + 4
C. y = 1/2x + 2
D. y = -1/2x + 4
5. Which is an equation of a line that is perpendicular to
the line graphed in question number 4?
A. y = 2x + 3
B. y = -2x + 3
C. y = ½ x + 1
D. y = -1/2x – 1
6. First street is perpendicular to L street. The equation
of L street on a map is represented by the equation
y =2x + 6. What is the equation representing
First Street if it passes through the point (4,5)?
A. y = -2x - 3 B. y = -2x + 5 C. y = 1/2x + 7 D. y =1/2 x+ 5
6 7. Line q passes through (6,4) and is perpendicular to
the graph of the line y= -2/3x +8. Which is the
equation of line q?
A.
y = -2/3x + 8
B.
y = 3/2x + 5
C.
y = 2/3x
D.
y = 3/2 x – 5
8. Given points A(7,8), B(5,-2) C(6,-8) and D(8,10)
which of the following is true?
A. is parallel to
is parallel to
B.
C.
is perpendicular to
D. None of these are true
Mastery Learning Algebra 1
Parallel/Perpendicular Lines, Distance/Midpoint
Midpoint of (x1, y1) and (x2, y2)
 x1  x2 y1  y 2 
,


2 
 2
Calculator: x 1 + x2 ENTER / 2
y1 + y2 ENTER / 2
(The average of the x’s and the average of the
y’s)
Ex: Find the midpoint of (3,2) & (4,1)
 3  4 2  1    1 3 
,

 , 
2   2 2
 2
Or: 3 + -4 ENTER / 2 and 2 + 1 ENTER /2
!!! Read question carefully, sometimes you are
given midpoint !!!
Ex: If the midpoint of (2,5) & ( x,3) is
( 2,4) Find the missing coordinate.
Do the following:
1) Plug in each answer choice OR
2) Graph the midpoint and the known point and
try to figure out where the other point is. OR
3) Set up the midpoint formula using given
information.   2  x , 5  3   2,4

2 
2
Only focus on the coordinate with the variable.
2 x
2
Set = to midpoint coordinate
2
1.
What can you add to -2 that will average to 2?
Solve. -2+x=4
X=6
Distance d 
( x 2  x1 ) 2  ( y 2  y1 ) 2
d  (rise) 2  (run) 2
Calculator: d 

(( x2  x1 ) 2  ( y2  y1 ) 2
Ex: Find the distance between
(6,2) & (3,1) Plug in numbers
d  (3  6) 2  (1  2) 2
d  (9) 2  (1) 2
d  81  1
d  9.06or 82
OR
((3  6) 2  (1  2) 2 = 9.06
Read question carefully, sometimes you are
given distance and must plug in your answer
choices.
9. Consider the line y = mx + b where m>0 and b>0.
What change occurs if m is multiplied by -1 and the
x-intercept remains the same?
A. The y-intercept becomes positive.
B. The y-intercept becomes negative.
C. The slope becomes positive.
D. The y-intercept remains the same.
10. Consider the line y = mx + b where m>0 and b>0.
Suppose that the x-intercept is increased and the slope
remains the same. What happens to the y-intercept?
A. It moves up.
B. It moves down.
C. It moves right. D. It moves left
11. On a map, Sarah’s house is located at (-4, 6) and
Jose’s house is located at (13, 7). What point is exactly
halfway in between Sarah and Jose?
A. (-2.5, 9.5) B. (-11,5) C. (30, 8) D. (4.5,6.5)
12. Points A and B have a midpoint M. A is
(9, 1) and M is (5, 3). Find the coordinates of B?
A. (7,2) B. (13, -1) C. (1, 5) D. (11.5, 2.5)
13. Points P (5,7) and Q(-3,9) are the enpoints of a
diameter of a circle. What are the coordinates of point
O, the center of the circle?
A. (1,8) B. (-1,8) C. (3.5,11.5) D. (-11,11)
14. The library is directly between the Post Office and
the local bank. The library is 3 blocks east and 2 blocks
south of the center of town. The Post Office is 1 block
east and 4 blocks north of the center of town. Find the
location of the local bank from the center of town.
A. 2 blocks east, 2 blocks north
B. 3 ½ blocks east, 0 blocks north
C. 1 block west, 8 blocks south
D. 5 blocks east, 8 blocks south
15. The coordinates of a square are (-3, -6), (3, 2),
(0, 5), (12,11). Find the area. (Round answer to the
nearest tenth.)
16. Find the perimeter of the triangle with points
(-5, 3), (4, 2), (7, -1). Round answer to nearest tenth.
17. What is the length between (-4, -5) and (5, 2)?
(Round the answer to the nearest tenth)
18. The distance between school and your house is
50 miles. If your house is located at (10, 1), find a
missing coordinate of school (x, 8).
A. 3 B. 11 C. 8 D. 50
Mastery Learning Algebra 1
Parallel/Perpendicular Lines, Distance/Midpoint