Name _____________________________________________________ Score
# 𝑐𝑜𝑟𝑟𝑒𝑐𝑡
# 𝑝𝑜𝑠𝑠𝑖𝑏𝑙𝑒
=
= 10 Period _________
Chapter 14 Test Review
Translate each given polygon such that one vertex of the image is located at the origin and label the vertices of the
image. Calculate the perimeter and area of the image.
Ex. Trapeziod ABCD.
𝐴′ 𝐵′ = 3, 𝐴′ 𝐷 ′ = 5, 𝐶 ′ 𝐷 ′ = 6
𝐵′ 𝐶 ′ = √(𝑥2 − 𝑥1 )2 + (𝑦2 − 𝑦1 )2
= √(6 − 3)2 + (0 − 5)2
= √(3)2 + (−5)2
= √9 + 25
= √34
𝑃𝑒𝑟𝑖𝑚𝑒𝑡𝑒𝑟 = 𝐴′ 𝐵′ + 𝐵′ 𝐶 ′ + 𝐶 ′ 𝐷 ′ + 𝐴′ 𝐷 ′
= 3 + √34 + 6 + 5
≈ 19.83 𝑢𝑛
𝑏1 = 𝐶 ′ 𝐷′ = 6, 𝑏2 = 𝐴′ 𝐵′ = 3, ℎ = 𝐴′ 𝐷 ′ = 5
1
𝐴𝑟𝑒𝑎 = (𝑏1 + 𝑏2 )ℎ
2
1
= (6 + 3)5
2
1
45
= (9)5 =
= 22.5 𝑢𝑛2
2
2
1. Trapezoid EFGH
Calculate the perimeter and area of each shape. No need to translate the figure to the origin.
2. Figure PQRST (Break it into two shapes)
3. Figure JKLMNOPQ (Take it into three shapes)
4. Figure ABCDEF (A lot of options here)
Double the area of each figure as shown. Calculate the area of both pre-image and image to verify.
5. Double the area of triangle HNW by manipulating the height. Label the image HN’W.
6. Double the area of triangle MFD by manipulating the base. Label the image M’FD
7. Double the area of parallelogram ABCD by manipulating the height. Label the image A’B’CD.
Use the Pythagorean Theorem to solve for the unknown side lengths.
8.
9.
10.
11.
Use the distance formula to calculate the distance between points.
12. The distance between (−3, 1) and (6, 2)
13. The distance between (4, 0) and (−5, −7)
Perform the indicated transformation on the coordinate plane.
15. Reflect triangle MDT over the x-axis to form triangle
14. Rotate triangle XYZ 90 counterclockwise about the
origin to form triangle DEF. Reflect triangle DEF over the
RJT. Rotate triangle RJT 180 clockwise about the origin
y-axis to form triangle MNO.
to form triangle XFZ.
List the coordinates of the image without graphing. List the rule used. Ex. (𝑥, 𝑦) → (𝑥 + 7, 𝑦 − 2) is a translation of 7
to the right and 2 down.
16. Triangle NPQ with coordinates N(12, -3), P(1, 2), and Q(9, 0) is rotated 90° counterclockwise about the origin.
17. Triangle PQR with coordinates P(3, -4), Q(6, -1), and R(6, -6) is translated 3 units to the left and 6 units up.