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 coordinates of original points

First, we find the coordinates of each vertex of the original figure:

• Point \( I \): From the graph, \( I(-2, 2) \)
• Point \( J \): \( J(-2, 1) \)
• Point \( F \): \( F(-1, -2) \)
• Point \( G \): \( G(1, -2) \)
• Point \( H \): \( H(2, -1) \)

Step2: Apply dilation factor (4) centered at origin

The rule for dilation centered at the origin with a scale factor \( k \) is \( (x, y) \to (k \cdot x, k \cdot y) \). Here, \( k = 4 \).

• For \( I(-2, 2) \): New coordinates \( I' = (4 \cdot (-2), 4 \cdot 2) = (-8, 8) \)
• For \( J(-2, 1) \): New coordinates \( J' = (4 \cdot (-2), 4 \cdot 1) = (-8, 4) \)
• For \( F(-1, -2) \): New coordinates \( F' = (4 \cdot (-1), 4 \cdot (-2)) = (-4, -8) \)
• For \( G(1, -2) \): New coordinates \( G' = (4 \cdot 1, 4 \cdot (-2)) = (4, -8) \)
• For \( H(2, -1) \): New coordinates \( H' = (4 \cdot 2, 4 \cdot (-1)) = (8, -4) \)

Step3: Plot the new points

Now, we plot the points \( I'(-8, 8) \), \( J'(-8, 4) \), \( F'(-4, -8) \), \( G'(4, -8) \), and \( H'(8, -4) \) on the coordinate plane and connect them in the same order as the original figure to get the dilated image.

Answer:

The dilated image has vertices at \( (-8, 8) \), \( (-8, 4) \), \( (-4, -8) \), \( (4, -8) \), and \( (8, -4) \). To plot the image, mark these points on the grid and connect them as per the original figure's shape.