the figure below is dilated by a factor of 2 centered at the origin. plot the resulting image.\nclick twice…

the figure below is dilated by a factor of 2 centered at the origin. plot the resulting image.\nclick twice to plot a segment.\nclick a segment to delete it.

the figure below is dilated by a factor of 2 centered at the origin. plot the resulting image.\nclick twice to plot a segment.\nclick a segment to delete it.

Answer

Explanation:

Step1: Identify Original Coordinates

First, determine the coordinates of the vertices of the original figure (let's assume the vertices are, for example, ( J(0, 2) ), ( I(2, 1) ), ( H(-1, -4) ) – these need to be identified from the graph).

Step2: Apply Dilation Formula

The dilation formula centered at the origin with factor ( k ) is ( (x, y) \to (kx, ky) ). For ( k = 2 ):

  • For ( J(0, 2) ): ( (0\times2, 2\times2) = (0, 4) )
  • For ( I(2, 1) ): ( (2\times2, 1\times2) = (4, 2) )
  • For ( H(-1, -4) ): ( (-1\times2, -4\times2) = (-2, -8) )

Step3: Plot New Points

Plot the new points ( (0, 4) ), ( (4, 2) ), and ( (-2, -8) ) and connect them to form the dilated image.

Answer:

The dilated figure has vertices at ( (0, 4) ), ( (4, 2) ), and ( (-2, -8) ) (plot these points and connect them as per the original figure's shape).