Question

the figure below is dilated with the center of dilation at the origin and a scale factor of $\frac{1}{3}$. what are the coordinates of the image of point b after this transformation?

Explanation:

Step1: Determine the coordinates of point B

From the graph, the coordinates of point B are \((-9,-6)\).

Step2: Apply the dilation formula

When a point \((x,y)\) is dilated with a scale factor \(k\) and center of dilation at the origin \((0,0)\), the formula for the image is \((kx,ky)\). Here \(k = \frac{1}{3}\), \(x=-9\), \(y = -6\).

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Answer:

\((-3,-2)\)