Question

what is the image of $(-9,3)$ after a dilation by a scale factor of $\frac{1}{3}$ 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 \(x=-9\), \(y = 3\), and \(k=\frac{1}{3}\).

Step2: Calculate new \(x\)-coordinate

Multiply the original \(x\)-coordinate by the scale factor: \(k\times x=\frac{1}{3}\times(-9)=- 3\).

Step3: Calculate new \(y\)-coordinate

Multiply the original \(y\)-coordinate by the scale factor: \(k\times y=\frac{1}{3}\times3 = 1\).

Answer:

\((-3,1)\)