Question

square abcd can be mapped onto the square pqrs by a dilation about the origin. 4. what is the scale factor of the dilation? a 4 b 6 c 12 d 16

Explanation:

Step1: Identify side - length of original and dilated squares

Let's assume the side - length of square \(ABCD\) is \(s_1\) and of square \(PQRS\) is \(s_2\). By counting the grid units, if we consider the horizontal or vertical sides, the side - length of square \(ABCD\) is \(2\) units and the side - length of square \(PQRS\) is \(8\) units.

Step2: Use the scale - factor formula

The scale factor \(k\) of a dilation is given by the ratio of the side - length of the dilated figure to the side - length of the original figure, \(k=\frac{s_2}{s_1}\).
Substitute \(s_1 = 2\) and \(s_2=8\) into the formula: \(k=\frac{8}{2}=4\).

Answer:

The scale factor of the dilation is \(4\), so the answer is A. 4.