Question

describe the transformation that maps figure abcd onto its image. figure abcd is dilated by a scale factor of $\frac{2}{3}$. the center of dilation is point ? a b c d

Explanation:

Step1: Recall dilation property

In a dilation, if a point \(P(x,y)\) is dilated by a scale - factor \(k\) with center of dilation \(O(a,b)\), the new point \(P'(x',y')\) is given by the formula \((x',y')=a + k(x - a),b + k(y - b)\). When the center of dilation is a vertex of the figure, that vertex and its image coincide.

Step2: Observe the figure

We see that point \(A\) and its image \(A'\) coincide. When the center of dilation is a vertex of the pre - image figure, that vertex does not move during the dilation process. Since the scale factor of dilation is \(\frac{2}{3}\) and point \(A\) and \(A'\) are the same, the center of dilation is point \(A\).

Answer:

A. \(A\)