Question

graph the image of rectangle qrst after a rotation 90° counterclockwise around the origin.

Explanation:

Step1: Identify original coordinates

The vertices of rectangle $QRST$ are:
$Q(-9, -8)$, $R(-4, -8)$, $S(-4, 0)$, $T(-9, 0)$

Step2: Apply 90° counterclockwise rotation rule

The rule for a 90° counterclockwise rotation around the origin is $(x, y) \to (-y, x)$.

• For $Q(-9, -8)$: $(-(-8), -9) = (8, -9)$
• For $R(-4, -8)$: $(-(-8), -4) = (8, -4)$
• For $S(-4, 0)$: $(-0, -4) = (0, -4)$
• For $T(-9, 0)$: $(-0, -9) = (0, -9)$

Step3: Plot new vertices and connect

Plot the points $Q'(8, -9)$, $R'(8, -4)$, $S'(0, -4)$, $T'(0, -9)$ on the coordinate plane, then connect them to form the rotated rectangle.

Answer:

The vertices of the rotated rectangle $Q'R'S'T'$ are $(8, -9)$, $(8, -4)$, $(0, -4)$, and $(0, -9)$. When plotted and connected, these form the 90° counterclockwise rotation of $QRST$ around the origin.