Question

the figure below is dilated by a factor of 3 centered at the origin. plot the resulting image. click twice to plot a segment. click a segment to delete it.

Explanation:

Step1: Identify original coordinates

First, find the coordinates of the vertices of the original figure. From the graph:

• \( O(-2, -3) \)
• \( P(2, -3) \)
• \( Q(3, 1) \)
• \( R(-1, 3) \)

Step2: Apply dilation factor

Dilation centered at the origin with a factor of \( 3 \) means we multiply each coordinate by \( 3 \). The formula for dilation \((x, y) \to (3x, 3y)\).

• For \( O(-2, -3) \): \( (3 \times -2, 3 \times -3) = (-6, -9) \)
• For \( P(2, -3) \): \( (3 \times 2, 3 \times -3) = (6, -9) \)
• For \( Q(3, 1) \): \( (3 \times 3, 3 \times 1) = (9, 3) \)
• For \( R(-1, 3) \): \( (3 \times -1, 3 \times 3) = (-3, 9) \)

Step3: Plot the new points

Plot the points \( (-6, -9) \), \( (6, -9) \), \( (9, 3) \), and \( (-3, 9) \) on the coordinate plane and connect them in the same order as the original figure.

Answer:

The vertices of the dilated figure are \( O'(-6, -9) \), \( P'(6, -9) \), \( Q'(9, 3) \), and \( R'(-3, 9) \). Plot these points and connect them to form the dilated image.