Question

graph the image of \\( \triangle qrs \\) after a rotation \\( 180^\circ \\) counterclockwise around the origin.

Explanation:

Step1: Identify original coordinates

From the graph: $Q(-4, -6)$, $R(-3, -3)$, $S(-1, -7)$

Step2: Apply 180° rotation rule

Rule: $(x,y)→(-x,-y)$
$Q'=(4,6)$, $R'=(3,3)$, $S'=(1,7)$

Step3: Plot rotated points

Mark $Q'(4,6)$, $R'(3,3)$, $S'(1,7)$ and connect them.

Answer:

The image of $\triangle QRS$ after 180° counterclockwise rotation around the origin has vertices at $(4,6)$, $(3,3)$, and $(1,7)$. (Plot these points to form the rotated triangle.)