Question

what is the image of (8, - 8) after a dilation by a scale factor of 1/4 centered at the origin?

Explanation:

Step1: Recall dilation formula

For a dilation centered at the origin with scale - factor \(k\), if the original point is \((x,y)\), the new point \((x',y')\) is given by \((x',y')=(k x,k y)\).

Step2: Identify values of \(x\), \(y\) and \(k\)

Here, \(x = 8\), \(y=-8\) and \(k=\frac{1}{4}\).

Step3: Calculate new coordinates

\(x'=k\times x=\frac{1}{4}\times8 = 2\) and \(y'=k\times y=\frac{1}{4}\times(-8)=-2\).

Answer:

\((2, - 2)\)