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.

Solution

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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