Question

what is the image of (0, - 3) after a dilation by a scale factor of 1/3 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 image point \((x',y')\) is given by \((x',y')=(k x,k y)\).

Step2: Identify the original point and scale - factor

The original point is \((0, - 3)\) and the scale - factor \(k=\frac{1}{3}\).

Step3: Calculate the coordinates of the image point

\(x'=k\times x=\frac{1}{3}\times0 = 0\)
\(y'=k\times y=\frac{1}{3}\times(-3)=-1\)

Answer:

\((0,-1)\)