Question

what are the coordinates of point c? (?, ?) △bcd is dilated by a scale factor of 1/3 with the center of dilation at the origin.

Explanation:

Step1: Find the original coordinates of point C

From the graph, the coordinates of point C are \((6,6)\).

Step2: Apply the dilation formula

The formula for dilation with scale factor \(k=\frac{1}{3}\) and center at the origin \((x,y)\to(kx,ky)\).
Substitute \(x = 6\) and \(y = 6\) into the formula:
\(x'=\frac{1}{3}\times6\), \(y'=\frac{1}{3}\times6\)
\(x' = 2\), \(y'=2\)

Answer:

\((2,2)\)