Questions: The figure below is dilated by a factor of 1/4 centered at the origin. Plot the resulting image. Click twice to plot a segment. Click a segment to delete it.

The figure below is dilated by a factor of 1/4 centered at the origin. Plot the resulting image. Click twice to plot a segment. Click a segment to delete it.
Transcript text: The figure below is dilated by a factor of $\frac{1}{4}$ centered at the origin. Plot the resulting image. Click twice to plot a segment. Click a segment to delete it.
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Solution

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Solution Steps

Step 1: Identify the coordinates of the vertices

The vertices of the triangle are:

  • A: (0, -8)
  • B: (8, 4)
  • C: (-8, 4)
Step 2: Apply the dilation factor

The dilation factor is \( \frac{1}{4} \). Multiply each coordinate by \( \frac{1}{4} \).

  • A' = \( (0 \cdot \frac{1}{4}, -8 \cdot \frac{1}{4}) = (0, -2) \)
  • B' = \( (8 \cdot \frac{1}{4}, 4 \cdot \frac{1}{4}) = (2, 1) \)
  • C' = \( (-8 \cdot \frac{1}{4}, 4 \cdot \frac{1}{4}) = (-2, 1) \)
Step 3: Plot the resulting image

Plot the new coordinates A' (0, -2), B' (2, 1), and C' (-2, 1) on the graph.

Final Answer

The resulting image after dilation has vertices at:

  • A' (0, -2)
  • B' (2, 1)
  • C' (-2, 1)
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