The coordinates of triangle ABC's vertices are located at (2, 3), (4,5), and (5,1), respectively. Triangle ABC is translated 5 units right and 3 units down, which we can call triangle A"5°C. Of the three
line segments formed by this translation, AA”, BB”, and CC", which is the shortest?

A. AA’
B.BB’
C.CC’
D. They are all the same length

Part A)

Using the Pythagorean theorem you can find the height:

17^2 = 8^2 + x^2

289 = 64 +x^2

x^2 = 289 - 64

x^2 = 225

x = √225

x = 15

The height is 15 cm.

Part B)

Area of the triangular side: 1/2 x 16 x 15 = 120 square cm.

There are two triangles so 120 x 2 = 240 square cm.

One side = 20 x 17 = 340

There are 2 sides so 340 x 2 = 680 square cm.

The bottom is 16 x 20 = 320 square cm.

Total cardboard needed: 240 + 680 + 320 = 1,240 square cm.