Question

AB has coordinates A(-15,5) and B(0-10). Find the coordinates of A' B'

after a dilation with a scale factor of centered at the origin.

Answer 1

`A'(-3,1)`

`B'(0,-2)`

Explanation:

By definition, a dilation is a transformation in which the sizes change but the shape of the image and the pre-image is the same.

In this case, you have the following coordinates of AB:

`A(-15,5) \\ B(0-10)`

You know that the scale factor (which can be represented with "k") that was used to dilate AB was:

`k=(1)/(5)`

And the dilation was centerered at the origin.

Therefore, in order to find the coordinates of the image A' B' you must multiply the coordinates of each point of the pre-image AB by the scale factor given.

Then, these are:

A'→
`(-15*(1)/(5),\ 5*(1)/(5))=(-3,1)`

B'→
`(0*(1)/(5),\ -10*(1)/(5))=(0,-2)`