Question

1. rectangle abcd is the image of rectangle abcd after a dilation. the center of dilation is the origin. what is the scale factor of the dilation? a. $\frac{1}{3}$ b. $\frac{2}{3}$ c. 2 d. 3

Explanation:

Step1: Find side - length of original rectangle

Count the grid - units for a side of rectangle \(ABCD\). For example, side \(AB\): The coordinates of \(A=(1,2)\) and \(B=(3,2)\), so \(AB = 3 - 1=2\).

Step2: Find side - length of dilated rectangle

Count the grid - units for the corresponding side of rectangle \(A'B'C'D'\). The coordinates of \(A'=(2,6)\) and \(B'=(8,6)\), so \(A'B'=8 - 2 = 6\).

Step3: Calculate the scale factor

The scale factor \(k\) of a dilation is given by the ratio of the length of a side of the dilated figure to the length of the corresponding side of the original figure. So \(k=\frac{A'B'}{AB}=\frac{6}{2}=3\).

Answer:

D. 3