Question

1. rotate the triangle 90° counterclockwise about the origin and draw the image. then label image with p, q, s.

Explanation:

Step1: Identify Coordinates

First, find the coordinates of \( P \), \( Q \), \( S \). From the graph: \( P(1, 0) \), \( Q(3, 0) \), \( S(0, 3) \) (assuming grid units, \( S \) is on \( y \)-axis at \( (0,3) \), \( P \) at \( (1,0) \), \( Q \) at \( (3,0) \)).

Step2: Apply 90° CCW Rotation Rule

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

• For \( P(1, 0) \): \( (1, 0) \to (0, 1) \) → \( P'(0, 1) \)
• For \( Q(3, 0) \): \( (3, 0) \to (0, 3) \) → \( Q'(0, 3) \)
• For \( S(0, 3) \): \( (0, 3) \to (-3, 0) \) → \( S'(-3, 0) \)

Step3: Plot and Draw

Plot the new points \( P'(0,1) \), \( Q'(0,3) \), \( S'(-3,0) \) and connect them to form the rotated triangle. Label the vertices as \( P' \), \( Q' \), \( S' \).

Answer:

The rotated triangle has vertices \( P'(0, 1) \), \( Q'(0, 3) \), \( S'(-3, 0) \) (plot these points and draw the triangle).