the figure below is dilated by a factor of 4 centered at the origin. plot the resulting image.\nclick twice…

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.