Question

What is the center of dilation? what is the scale factor of the dilation?

Answer 1

Answer: Dilation with scale factor 2, multiply by 2.

(x, y) → (2x,2y)

Explanation:

A description of a dilation includes the scale factor (or ratio) and the center of the dilation. The center of dilation is a fixed point in the plane. If the scale factor is greater than 1, If the scale factor is between 0 and 1,

Answer 2

a. The center of dilation is (0,0).

b. The scale factor of the dilation is 2.

Explanation:

If the rule of dilation is

`(x,y)\rightarrow (kx,ky)` ... (1)

then the center of dilation is origin and scale factor is k.

From the given graph it is clear that the vertices of triangle ABC are A(-2,2), B(4,2) and C(-2,-2).

The vertices of triangle A'B'C' are A'(-4,4), B'(8,4) and C'(-4,-4).

The relation between preimage and image is defined as

`(x,y)\rightarrow (2x,2y)` .... (2)

It means center of dilation is (0,0).

On comparing (1) and (2), we get

`k=2`

Therefore, the scale factor of the dilation is 2.