Question

ABC was dilated to create A' B' C'. What is the center of dilation? And what is the scale factor of the dilation?

Answer 1

Given:

In the given figure the vertices of triangle ABC are A(-2,2), B(4,2), C(-2,-2).

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

To find:

The center of dilation and the scale factor.

Solution:

In the given graph, draw the lines AA', BB' and CC'. The intersection point of these lines is the center of dilation.

From the below graph, it is clear that the lines AA', BB' and CC' intersect each other at (0,0).

Therefore, the center of dilation is (0,0).

If a figure is dilated by factor k and the center of dilation is origin, then

$(x,y)\to (kx,ky)$

$A(-2,2)\to A'(k(-2),k(2))$

$A(-2,2)\to A'(-2k,2k)$

It is given that A'(-4,4). So,

$(-2k,2k)=(-4,4)$

On comparing both sides, we get

$-2k=-4$

$2k=4$

$k=\dfrac{4}{2}$

$k=2$

Therefore, the scale factor is 2.