MMB 6.5 Tessellations page 713 – 716 #1 – 14
Objective: Indentify a tessellation; perform a transformation on a given figure.
Definition: A tessellation (or tiling) is a repeating pattern of shapes that covers an entire plane and fits
together without gaps or overlaps.
Definition: A polygon is a closed figure having three or more line segments as sides. A regular polygon is a
polygon having all sides the same length and all interior angles of equal measure.
Only three regular polygons can be used to form tessellations; equilateral triangles, squares, or regular
hexagons.
1. Graph each point and its image under a reflection i
n the x-axis. Write the coordinates of the image point.
a. (3, 2)
b. (4, -1)
c. (-2, 4)
d. (-1, -3)
e. (0, 3)
f. (0,-5)
2. Graph each point and its image under a
Reflection in the y-axis. Write the coordinates of the image point.
a. (2, 1)
b. (3, -2)
c. (-1, 4)
d. (-2, -3)
e. (-2, 0)
e. (5, 0)
3. Graph each point. Graph its reflection over the
Indicated axis a) x – axis b) y – axis .
Write the coordinates of the reflected point.
i. (3, -1)
ii. (-4, 2)
iii. (5, 3)
iv. (-1. -3)
4. Graph triangle ABC having coordinates A(1,4), B(5,5), C(3,1).
a. Graph the reflection of the image A’B’C’, over the y axis.
b. What are the coordinates of the reflection triangle A’B’C’.
c. Graph the reflection of the triangle A’B’C’, over the x-axis.
d. Write the coordinates of the reflection triangle
A”B”C”
e. Describe the differences about ABC, triangle
A’,B’, C’ and triangle A”B”C”.
5. Graph each point and its reflection in the origin.
what are the coordinates of the image point?
a. (4, 3)
b. (1, -2)
c. (-2, 3)
d. (-3, -1)
e. (0, -4)
f. (x, y)
6. Graph each point and its reflection as indicated. T
hen, write the coordinates of the reflected point.
a. (2, 5), x – axis
b. (-3, 4), y –axis
c. (-2, -1), x-axis
d. (-1, 2), origin
e. (4, 1), y – axis
f. (2, -3), origin
g. (x, y), origin
h. (x, y), y-axis
i. (x, y) origin
7. The vertices of the polygon ABCD are A(3, 4), B(7, 4), C(6, 1), d(2, 1).
a. What is the name of this polygon?
b. Graph the polygon and its reflection over the x-axis.
c. What are the coordinates of the reflected polygon?
d. Graph the polygon and its reflection over the y-axis.
e. What are the coordinates of the reflected polygon?
f. Graph the polygon and its reflection in the origin.
g. What are the coordinates of the reflected polygon?
h. What is the area of the polygon ABCD?
i. What is the area of polygon A’B’C’D’?
j. Whis the perimeter (to the nearest hundredth) of polygon ABCD?
k. What is the perimeter (to the nearest hundredth) of polygon A”B”C”D”?
8. Translate each point left 3 units and up 2 units.
a. What are the coordinates of each image point?
A(3,2)
B(3, -2)
C(-2,-1)
D(-4,1)
b. Graph each point and its image.
c. Connect points ABCD, what type of polygon is this?
d. What is the area of the polygon ABCD?
e. What is the area of polygon A’B’C’D’?
9. The vertices of triangle ABC are
A(-4, -1), B(-3, -2), C(-1,0).
a. Translate triangle ABC right 5 units and up 4 units
b. Write the coordinates of the image A’B’C’.
c. Graph triangle ABC and triangle A’B’C’.
d. In which quadrant(s) is triangle ABC located?
e. In which quadrant(s) is triangle A’B’C’ located?
f. Translate triangle ABC right 2 units and down 3 units.
g. Write the coordinates of the image A”B”C”.
h. graph triangle A”B”C”.
i. In which quadrant(s) is triangle A”B”C” located?
10. Graph each point and its image. What are the
coordinates of the image?
a. P(2, 4); right 2 units, down 1 unit.
b. Q(-1, 3); right 4 units, down 4 units.
c. R(3, -2); left 5 units, up 3 units.
d. S(-4, -5); right 1 unit, up 7 units.
11. Graph triangle ABC with vertices A(2,4), B(5,3), and C(2,-1). Graph the image for the transformation
describe below. Name the coordinates of the vertices of
image.
a. Translated left 5 units, down 4 units.
b. Translated right t1 unit, down 3 units.
c. Reflected over the y axis.
d. What is the area of triangle ABC?
e. What is the area of triangle A’B’C’?
f. what is the area of triangle A”B”C”?
12. If a triangle is in Quadrant I, in which quadrant will it be after the indicated counterclockwise rotation?
a. 90°
b. 180°
c. 270°
d. 810°
the
13. Graph each point. rotate the point counterclockwise about the origin in the given number of degrees.
Write the coordinates of the image.
a. (-5, -2), 90°
b. (3, 4), 270°
c. (2, -1), 180°
d. (-1, 3), 90°
14. The given point is rotated counterclockwise 90°, 180°, and 270° about the origin. Give the coordinates of
each image.
a. (1, -3)
b. (-4,-2)
c. (-5, 2)
90°
180°
270°