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 points C, D, E, F from the graph.

• \( C(0, -2) \)
• \( D(1, -2) \)
• \( E(3, 2) \)
• \( F(-3, 1) \)

Step2: Apply dilation factor (k=3)

Dilation centered at origin: \((x,y) \to (kx, ky)\). Multiply each coordinate by 3.

• \( C': (0\times3, -2\times3) = (0, -6) \)
• \( D': (1\times3, -2\times3) = (3, -6) \)
• \( E': (3\times3, 2\times3) = (9, 6) \)
• \( F': (-3\times3, 1\times3) = (-9, 3) \)

Step3: Plot the new points

Plot \( C'(0, -6) \), \( D'(3, -6) \), \( E'(9, 6) \), \( F'(-9, 3) \) and connect them as per the original figure's shape.

Answer:

The dilated image has vertices at \( (0, -6) \), \( (3, -6) \), \( (9, 6) \), and \( (-9, 3) \). Plot these points and connect them to form the dilated figure.