Question

13 graph the image of δabc after ( r_{(90^circ, o)} )

Explanation:

Step1: Identify Coordinates

First, find coordinates of \( A \), \( B \), \( C \). From graph: \( A(1, 0) \), \( B(0, 2) \), \( C(-3, 0) \).

Step2: Apply 90° Rotation Rule

The rule for \( R_{(90^\circ, O)} \) (rotation 90° counterclockwise about origin) is \( (x, y) \to (-y, x) \).

• For \( A(1, 0) \): \( (-0, 1) = (0, 1) \)
• For \( B(0, 2) \): \( (-2, 0) \)
• For \( C(-3, 0) \): \( (-0, -3) = (0, -3) \)

Step3: Plot New Points

Plot \( A'(0, 1) \), \( B'(-2, 0) \), \( C'(0, -3) \) and connect to form \( \triangle A'B'C' \).

Answer:

The image \( \triangle A'B'C' \) has vertices at \( A'(0, 1) \), \( B'(-2, 0) \), \( C'(0, -3) \) (plotted and connected as a polygon).