Question

what is the image of $(-12,-12)$ after a dilation by a scale factor of $\frac{1}{4}$ centered at the origin?

Explanation:

Step1: Apply dilation formula

For a point \((x,y)\) dilated by a scale factor \(k\) centered at the origin, the new point is \((kx,ky)\). Here \(x=-12\), \(y = -12\), and \(k=\frac{1}{4}\).

Step2: Calculate new \(x\)-coordinate

Multiply \(x\)-coordinate by \(k\): \(\frac{1}{4}\times(-12)=- 3\).

Step3: Calculate new \(y\)-coordinate

Multiply \(y\)-coordinate by \(k\): \(\frac{1}{4}\times(-12)=-3\).

Answer:

\((-3,-3)\)