Question

Given the preimage and image, find the dilation scale factor​

Answer 1

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

$-2k=-4$

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

$k=2$

Therefore, the dilation scale factor is 2.