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 \((8, 2)\).

Step2: Apply the dilation formula

The formula for dilation with center at the origin \((0,0)\) and scale factor \(k=\frac{1}{3}\) is \((x,y)\to(kx,ky)\).
Substitute \(x = 8\) and \(y = 2\) into the formula:
\(x'=\frac{1}{3}\times8=\frac{8}{3}\), \(y'=\frac{1}{3}\times2=\frac{2}{3}\)

Answer:

\((\frac{8}{3},\frac{2}{3})\)