Question

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

Explanation:

Step1: Determine the coordinates of point \(D\)

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

Step2: Apply the dilation formula

When a point \((x,y)\) is dilated by a scale factor \(k\) with the center of dilation at the origin \((0,0)\), the formula for the new coordinates \((x',y')\) is \(x' = kx\) and \(y'=ky\). Here \(k = \frac{1}{3}\), \(x = 9\), \(y = 3\).
So \(x'=\frac{1}{3}\times9 = 3\) and \(y'=\frac{1}{3}\times3=1\).

Answer:

\((3,1)\)