Question

the figure below is dilated by a factor of 4 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 each vertex:

• \( P(-1, -1) \)
• \( Q(0, -2) \)
• \( R(2, 0) \)
• \( S(0, 2) \)
• \( T(-1, 2) \)

Step2: Apply dilation factor (4)

Dilation centered at the origin with factor \( k \) transforms \( (x, y) \) to \( (k \cdot x, k \cdot y) \). So:

• For \( P(-1, -1) \): \( (4 \cdot (-1), 4 \cdot (-1)) = (-4, -4) \)
• For \( Q(0, -2) \): \( (4 \cdot 0, 4 \cdot (-2)) = (0, -8) \)
• For \( R(2, 0) \): \( (4 \cdot 2, 4 \cdot 0) = (8, 0) \)
• For \( S(0, 2) \): \( (4 \cdot 0, 4 \cdot 2) = (0, 8) \)
• For \( T(-1, 2) \): \( (4 \cdot (-1), 4 \cdot 2) = (-4, 8) \)

Step3: Plot the new points

Plot the points \( (-4, -4) \), \( (0, -8) \), \( (8, 0) \), \( (0, 8) \), \( (-4, 8) \) and connect them as per the original figure's shape.

Answer:

The dilated image has vertices at \( (-4, -4) \), \( (0, -8) \), \( (8, 0) \), \( (0, 8) \), \( (-4, 8) \). Plot these points and connect them to form the dilated figure.