the figure below is dilated by a factor of 3 centered at the origin. plot the resulting image.\nclick twice…

the figure below is dilated by a factor of 3 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 3 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, find the coordinates of each vertex:

  • ( S(-3, -3) )
  • ( T(1, -3) )
  • ( U(3, 0) )
  • ( V(3, 2) )
  • ( W(-3, 3) )

Step2: Apply Dilation Formula

The dilation formula centered at the origin with scale factor ( k ) is ( (x, y) \to (kx, ky) ). Here, ( k = 3 ).

  • For ( S(-3, -3) ): ( (3 \times -3, 3 \times -3) = (-9, -9) )
  • For ( T(1, -3) ): ( (3 \times 1, 3 \times -3) = (3, -9) )
  • For ( U(3, 0) ): ( (3 \times 3, 3 \times 0) = (9, 0) )
  • For ( V(3, 2) ): ( (3 \times 3, 3 \times 2) = (9, 6) )
  • For ( W(-3, 3) ): ( (3 \times -3, 3 \times 3) = (-9, 9) )

Step3: Plot the New Points

Plot the points ( (-9, -9) ), ( (3, -9) ), ( (9, 0) ), ( (9, 6) ), and ( (-9, 9) ) on the coordinate plane and connect them in the same order as the original figure.

Answer:

The resulting image has vertices at ((-9, -9)), ((3, -9)), ((9, 0)), ((9, 6)), and ((-9, 9)) (plotted and connected appropriately).