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: Find side - length of original square

Count the grid units for a side of square \(ABCD\). For example, the distance between \(A(2,2)\) and \(B(2, - 2)\) is \(|2-( - 2)|=4\) units.

Step2: Find side - length of dilated square

Count the grid units for a side of square \(PQRS\). For example, the distance between \(P(8,8)\) and \(Q(8, - 8)\) is \(|8-( - 8)| = 16\) units.

Step3: Calculate scale factor

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. So \(k=\frac{\text{side - length of }PQRS}{\text{side - length of }ABCD}=\frac{16}{4}=4\).

Answer:

A. 4