Question

what is the image of $(-9,-12)$ after a dilation by a scale factor of $\frac{1}{3}$ centered at the origin?

Explanation:

Step1: Apply the dilation formula

For a point \((x,y)\) dilated by a scale factor \(k\) centered at the origin, the new point \((x',y')\) is given by \(x' = kx\) and \(y'=ky\). Here \(x=-9\), \(y = - 12\), and \(k=\frac{1}{3}\).

Step2: Calculate the \(x\) - coordinate of the image

\(x'=\frac{1}{3}\times(-9)=- 3\)

Step3: Calculate the \(y\) - coordinate of the image

\(y'=\frac{1}{3}\times(-12)=-4\)

Answer:

\((-3,-4)\)