Question

triangle qrs is dilated according to the rule $d_{o,2} (x,y)$. what is true about the image $\delta qrs$? select three options. which statements are true? $\square$ $d_{o,2} (x,y) = (2x, 2y)$ $\square$ side qs lies on a line with a slope of -1. $\square$ $\overline{qr}$ is longer than $\overline{qr}$. $\square$ the vertices of the image are closer to the origin than those of the pre - image. $\square$ the distance from q to the origin is twice the distance from q to the origin.

Explanation:

Step1: Recall dilation rule

$D_{O,2}(x,y)=(2x,2y)$ (scale factor 2, origin center). Check first option: true.

Step2: Find image vertices

$Q(-3,3)\to Q'(-6,6)$, $S(-1,1)\to S'(2,2)$ (wait, correction: $S(-1,1)\to S'(-2,2)$). Slope of $Q'S'$: $\frac{2-6}{-2-(-6)}=\frac{-4}{4}=-1$. Check second option: true.

Step3: Compare segment lengths

Dilation with scale factor >1 increases length. $\overline{QR}$ (pre-image) < $\overline{Q'R'}$ (image). Third option: false.

Step4: Check distance from origin

Scale factor 2 means image vertices are farther. Fourth option: false.

Step5: Distance ratio

Distance from origin scales by 2. $Q'$ distance = 2×$Q$ distance. Fifth option: true.

Answer:

A. $D_{O,2}(x,y)=(2x,2y)$, B. Side $Q'S'$ lies on a line with a slope of -1, E. The distance from $Q'$ to the origin is twice the distance from $Q$ to the origin.