Question

Rectangle A′B′C′D′ is the image of rectangle ABCD after a dilation.

Answer 1

The scale factor of the dilation from ABCD to A′B′C′D′ is 3.

Explanation:

• In the smaller rectangle, ABCD the length of the rectangle is 4 - 1 = 3 units, while the width of the rectangle is 5 - 1 = 4 units. For the larger rectangle, A′B′C′D′ the rectangle's length is 12 - 3 = 9 units and the rectangle's width is 15 - 3 = 12 units.

• To determine the scale factor, we divide the measurement after scaling by the same measurement before scaling. In this case, it can either be the rectangle's length or width.                                                                    So the scale factor = $\frac{lengthafterdilation}{lengthbeforedilation}$  = $\frac{9}{3}$ = 3.                                                             While the scale factor for width = $\frac{widthafterdilation}{widthbeforedilation}$ = $\frac{12}{4}$ = 3.

• So the rectangle ABCD is dilated by a scale factor of 3 to produce rectangle A′B′C′D′.