Question

describe the transformation that maps figure efgh onto its image. figure efgh is dilated by a scale factor of 2. the center of dilation is at? point e point f the origin

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 \(C(a,b)\), the coordinates of the image \(P'(x',y')\) are given by \(x'=a + k(x - a)\) and \(y'=b + k(y - b)\). If the center of dilation is a point on the figure, that point and its image coincide.

Step2: Observe the figure

We see that point \(E\) and its image \(E'\) coincide. When the center of dilation is a point on the pre - image figure, that point remains fixed under dilation. Since point \(E\) is fixed and the figure \(EFGH\) is dilated by a scale factor of 2, the center of dilation is point \(E\).

Answer:

point \(E\)