Question

what are the coordinates of point d? △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 D

From the graph, the original coordinates of point \(D\) are \((3,9)\)

Step2: Apply the dilation formula

The formula for dilation with center at the origin \((x,y)\to(kx,ky)\), where \(k = \frac{1}{3}\)
For \(x = 3\) and \(y=9\), we have \(kx=\frac{1}{3}\times3 = 1\) and \(ky=\frac{1}{3}\times9 = 3\)

Answer:

\((1,3)\)