Question

Triangle ABC has vertices point A(- 2, 4) point B(- 6, 8) and point C(- 2,4) After dilation, triangle A' * B' * C' has vertices point A' * (- 1, 2) point B' * (- 3, 4) and point C' * (- 1, 2) Determine the scale factor for the dilation of triangle ABC with a center point of dilation at the origin (0, 0) (1 point)

- 1/2

1/2

0-2

02

Answer 1

To determine the scale factor for the dilation, we can calculate the distance between two corresponding points before and after the dilation.

Before dilation:
Distance between A and B: √((-6-(-2))^2 + (8-4)^2) = √((-4)^2 + 4^2) = √(16 + 16) = √32
Distance between B and C: √((-2-(-6))^2 + (4-8)^2) = √((4)^2 + (-4)^2) = √(16 + 16) = √32

After dilation:
Distance between A' and B': √((-3-(-1))^2 + (4-2)^2) = √((-2)^2 + 2^2) = √(4 + 4) = √8
Distance between B' and C': √((-1-(-3))^2 + (2-4)^2) = √((2)^2 + (-2)^2) = √(4 + 4) = √8

Since the distances before and after the dilation are equal (both are √32 and √8), the scale factor is the square root of the ratio of these distances: √(8/32) = √(1/4) = 1/2.

Therefore, the scale factor for the dilation of triangle ABC with a center point of dilation at the origin is 1/2.