Name _____________________________________________________ Score
# 𝑐𝑜𝑟𝑟𝑒𝑐𝑡
# 𝑝𝑜𝑠𝑠𝑖𝑏𝑙𝑒
=
= 10 Period _________
14.2 – Area and Perimeter of Triangles on the Coordinate Plane
Determine the area of each given triangle on the coordinate plane. Round your answer to the nearest hundredth, if
necessary.
Ex. Triangle WXY.
1. Triangle ACE
2. Triangle JKL
Double the area of each triangle as directed. Label the image then calculate the area of the pre-image and the area of
the image to verify your solution.
Ex. Double the area of triangle DMP by manipulating the height. Label the image DM’P.
3. Double the area of triangle MLP manipulating the height. Label the image MLP’.
̅̅̅̅ is the height of triangle EFG, and Beth claims that 𝐺𝐽
̅̅̅ is the height of triangle EFG.
4. Cisco claims that 𝐺𝐻
a. Who is correct? Support your answer with mathematics.
b. Calculate the area of triangle EFG. Show your work.
Use the Pythagorean Theorem to solve for the unknown side lengths.
5.
6.
7.
8.
9. A few years ago, Leon planted a small triangular garden in his backyard. Recently he has been thinking that the garden
is too small. He now wants to double the area of the garden. His original garden is shown on the coordinate plane. Each
unit represents one square foot.
a. Describe two ways Leon could double the area of his garden.
b. Because of the location of Leon’s neighbors, he cannot extend the garden any further horizontally. Use this
information to manipulate the image POD representing Leon’s garden to double the area. Label the image as PO’D.
c. Determine the area of the original garden and the new garden to verify that the area has doubled.
Use the distance formula to verify the solution. Show all work.
10. The distance between (2, 2) and (8, 5) ≈ 6.71 𝑢𝑛.
11. The distance between (3, 7) and (7, 3) ≈ 5.66 𝑢𝑛.
12.
The distance between (−6, 8) and (6, 3) = 13 𝑢𝑛.
13. The distance between (7, 5) and (3, −3) ≈ 8.94 𝑢𝑛.