Question

if Q(-3,4), R(-2,-1),T(3,1),W(3,5) is a quadrilateral and Q'(-27,36) is the image of Q under a dilation centered at the origin, find W'

Answer 1

W'(27,45)

Explanation:

First we must fnd the scale factor of the dilation and then multiply the coordinates of W(3,5) by the scale factor.

Let k be the scale factor of the dilation centered at the origin.

The mapping for a dilation by a scale factor k is

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

`Q( - 3,4)\to Q'( - 3k,4k)`

But we were given the coordinates of the image, which is

Q'(-27,36)

Comparing coordinates:

`4k = 36`

`\implies \: k = 9`

We could compare the first coordinates too and get the same result.

The image of W(3,5) is given by:

`W(3,5) \to \: W'(3 * 9,5 * 9)`

`W(3,5) \to \: W'(27,45)`