Question

square abcd is dilated using the origin as the center of dilation to create square abcd. what rule best represents the dilation applied to square abcd to create square abcd? a (x, y)→(4x, 4y) b (x, y)→(1/4x, 1/4y) c (x, y)→(2x, 2y) d (x, y)→(1/2x, 1/2y)

Explanation:

Step1: Identify side - length ratio

Count the side - length of square ABCD and A'B'C'D'. Suppose side - length of ABCD is 4 units and of A'B'C'D' is 2 units. The ratio of side - length of A'B'C'D' to ABCD is $\frac{2}{4}=\frac{1}{2}$.

Step2: Recall dilation rule

The general rule for dilation with center at the origin is $(x,y)\to(kx,ky)$, where $k$ is the scale factor. Since $k = \frac{1}{2}$, the rule is $(x,y)\to(\frac{1}{2}x,\frac{1}{2}y)$.

Answer:

D. $(x,y)\to(\frac{1}{2}x,\frac{1}{2}y)$