Question

part one: read the instructions
a. rotate triangle abc 90° clockwise about the origin.

Explanation:

Step1: Find coordinates of A, B, C

From the graph, \( A(-5, 3) \), \( B(-2, 1) \), \( C(-5, 1) \).

Step2: Apply 90° clockwise rotation rule

The rule for rotating a point \((x, y)\) 90° clockwise about the origin is \((x, y) \to (y, -x)\).

• For \( A(-5, 3) \): New coordinates \( A'(3, 5) \) (since \( x=-5, y = 3 \); \( y = 3 \), \( -x=5 \)).
• For \( B(-2, 1) \): New coordinates \( B'(1, 2) \) (since \( x=-2, y = 1 \); \( y = 1 \), \( -x=2 \)).
• For \( C(-5, 1) \): New coordinates \( C'(1, 5) \) (since \( x=-5, y = 1 \); \( y = 1 \), \( -x=5 \)).

Step3: Plot the rotated points

Plot \( A'(3, 5) \), \( B'(1, 2) \), \( C'(1, 5) \) and connect them to form the rotated triangle.

Answer:

The rotated triangle \( A'B'C' \) has vertices at \( A'(3, 5) \), \( B'(1, 2) \), \( C'(1, 5) \) (plotted on the coordinate plane as per the rotation rule).