Question

1. a(-10,-8) is the image of a after a dilation centered at the origin with a scale factor of 2. what are the coordinates of a?

Explanation:

Step1: Recall the dilation formula

If a point \(A(x,y)\) is dilated about the origin with a scale factor \(k\), the image \(A'(x',y')\) is given by \(x' = kx\) and \(y'=ky\). Here \(k = 2\), \(x'=- 10\), \(y'=-8\).

Step2: Solve for \(x\) and \(y\)

Since \(x'=kx\), then \(x=\frac{x'}{k}\). Substituting \(x'=-10\) and \(k = 2\), we get \(x=\frac{-10}{2}=-5\).
Since \(y'=ky\), then \(y=\frac{y'}{k}\). Substituting \(y'=-8\) and \(k = 2\), we get \(y=\frac{-8}{2}=-4\).

Answer:

The coordinates of \(A\) are \((-5,-4)\)