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 of the original figure. Let's assume the coordinates (from the graph, estimating):

• Point F: \((0, 1)\)
• Point E: \((1, 1)\)
• Point D: \((1, -1)\)
• Point C: \((0, -2)\)
• Point B: \((-1, -1)\)

Step2: Apply Dilation Factor

Dilation centered at the origin with factor \(k = 4\) means each coordinate \((x, y)\) becomes \((4x, 4y)\).

• For F: \(4\times0 = 0\), \(4\times1 = 4\) → \((0, 4)\)
• For E: \(4\times1 = 4\), \(4\times1 = 4\) → \((4, 4)\)
• For D: \(4\times1 = 4\), \(4\times(-1) = -4\) → \((4, -4)\)
• For C: \(4\times0 = 0\), \(4\times(-2) = -8\) → \((0, -8)\)
• For B: \(4\times(-1) = -4\), \(4\times(-1) = -4\) → \((-4, -4)\)

Step3: Plot the New Points

Plot the points \((0, 4)\), \((4, 4)\), \((4, -4)\), \((0, -8)\), \((-4, -4)\) and connect them to form the dilated figure.

Answer:

The dilated figure has vertices at \((0, 4)\), \((4, 4)\), \((4, -4)\), \((0, -8)\), \((-4, -4)\) (plot these points and connect them).