Question

what coordinate expression represents the coordinates of any point after dilation by any scale factor, a?

Answer 1

(x,y) → (ax,ay) .

Explanation:

A dilation is a transformation that changes the size of the image. It either shrink or enlarge a shape by using a scale factor about a center of dilation.

If we transform point (x,y) by using dilation with scale factor k (assume center of dilation at (0,0) then the coordinate of the image will be (kx,ky).

So, the coordinate expression represents the coordinates of any point after dilation by a scale factor of a:

(x,y) → (ax,ay) .

Answer 2

`\huge\boxed{(ax, ay)}`

Explanation:

In order to dilate the coordinates of a point, we want to make it
`a` times bigger. In order to do this, we can multiply the x and y values by our scale factor, a. This is called mapping. What it does is it basically multiplied our points by a specific number so that we end up with a figure that is
`a` (the scale factor) times bigger than the original.

So in order to make an expression for this, we multiply the x and y coordinates by a. So we have ax and ay.

Hope this helped!