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)

Question

1/2

-2

-1/2

2

Answer 1

To determine the scale factor for the dilation, we can compare the lengths of corresponding sides between the two triangles.

The distance formula can be used to find the length of a side between two points:

AB = √((-6 - (-2))^2 + (8 - 4)^2) = √(16 + 16) = √32
A'B' = √((-3 - (-1))^2 + (4 - 2)^2) = √(4 + 4) = √8

The scale factor for the dilation can be found by dividing the length of the corresponding side of A'B' by the length of AB:

Scale factor = A'B' / AB = (√8) / (√32) = √(8/32) = √(1/4) = 1/2

Therefore, the scale factor for the dilation of triangle ABC is 1/2.