Question

dilation the center of dilution is the origin b (2,3) and B(-4,-6) what is the scale factors of this dilation that transformed a B into B​

Answer 1

Given:

Consider the two points are B(2,3) and B'(-4,-6).

Center of dilation is the origin.

To find:

The scale factors of this dilation that transformed B into B'.​

Solution:

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

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

It means, the point after dilation is

$(x',y')=(kx,ky)$

where, k is the scale factor.

$k=\dfrac{x'}{x}$

x-coordinate of image is -4 and x-coordinate of original point is 2.

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

$k=-2$

Therefore, the scale factor is -2. It means, the point and image lie on the opposite sides of center of dilation.