Question

Suppose that triangle ABC is dilated to A’B'C’ by a scale factor of 1/2 with a center of dilation at the origin. What is the distance from the center of dilation to vertex A’?

Answer 1

Answer with explanation:

The coordinates of vertices of triangle ABC is not important for this question.

It is also not important in which quadrant the triangle ABC is lying to answer this question.

If the ΔABC is dilated by a factor of ,
`(1)/(2)` to obtain ΔA'B'C' having center of dilation at the origin.

When Dilation takes place,

1. ΔABC→ (Pre Image) ~ ΔA'B'C'→(Image)

2. Shape does not change but size changes and size of image( ΔABC) will be smaller than Size of Preimage( ΔA'B'C').

3. Sides of two triangles that is image and Preimage are proportional,
`=(1)/(2)`,

`(OA)/(OA')=(2)/(1)`

→OA=2 × OA'

`OA'=(OA)/(2)`