Given the preimage and image, find the dilation scale factor

Question

asked Mar 28, 2022 212k views

1 Answer

Muffe · Answer 1 · 2022-04-03T09:19:54+0000

Given:

The preimage and image of a triangle in the given figure.

To find:

The dilation scale factor.

Solution:

From the given figure it is clear that the vertices of the triangle ABC are A(-2,-2), B(-1,2) and C(2,1).

The vertices of the triangle A'B'C' are A'(-4,-4), B'(-2,4) and C'(4,2).

If a figure is dilated by factor K with (0,0) as the center of dilation, then

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

Let the scale factor be K, then the image of point A is:

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

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

From the given figure it is clear that the image of point A is A'(-4,-4).

A'(-2k,-2k)=A'(-4,-4)

On comparing both sides, we get

-2k=-4

k=(-4)/(-2)

k=2

Therefore, the dilation scale factor is 2.