Question

g.2

1. point t is located at (-8, 5). point t is rotated $90^\circ$ counterclockwise, then reflected across the y-axis. what are the coordinates of t? sketch a simple coordinate plane to prove your answer.

Explanation:

Step1: Rotate 90° counterclockwise

For a point $(x,y)$, 90° counterclockwise rotation gives $(-y,x)$.
For $T(-8,5)$: $(-5, -8)$

Step2: Reflect across y-axis

For a point $(x,y)$, reflection over y-axis gives $(-x,y)$.
For $(-5, -8)$: $(5, -8)$

Step3: Sketch verification

1. Plot original $T(-8,5)$ in Quadrant II.
2. Plot rotated point $(-5,-8)$ in Quadrant III.
3. Plot final $T''(5,-8)$ in Quadrant IV.

The coordinate plane sketch confirms the transformations:

Quadrant	Point	Coordinates
III	Rotated $T$	$(-5,-8)$
IV	$T''$	$(5,-8)$

Answer:

The coordinates of $T''$ are $\boldsymbol{(5, -8)}$