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Schoolnet Practice 1/20/21 1 1 of 10
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Triangle XYZ has vertices at X(3, 2), Y(8, 2), and Z(3, 6). The triangle will be dilated by a scale factor of 4.
What is the difference between the area of triangle X'Y'Z' and the area of triangle XYZ?

9514 1404 393

  150 square units

Step-by-step explanation:

The base of ΔXYZ is XY, 8-3 = 5 units in length. The height of ΔXYZ is XZ, 6-2 = 4 units in length. The area of ΔXYZ is then ...

  A = 1/2bh

  A = 1/2(5)(4) = 10 . . . . . square units

The area of a figure is multiplied by the square of the dilation factor, so the area of ΔX'Y'Z' is 4²×10 = 160 square units

The difference between the areas is ...

  160 - 10 = 150 . . . . . square units difference