To find the new coordinates of the vertices of the parallelogram after dilating with respect to the origin by a magnitude of 2, we multiply the coordinates of each vertex by 2.
The original vertices are:
- A(-2, -1)
- B(-3, 2)
- C(1, 3)
- D(2, 0)
Now we will dilate each vertex:
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For A(-2, -1): \[ A' = (2 \times -2, 2 \times -1) = (-4, -2) \]
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For B(-3, 2): \[ B' = (2 \times -3, 2 \times 2) = (-6, 4) \]
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For C(1, 3): \[ C' = (2 \times 1, 2 \times 3) = (2, 6) \]
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For D(2, 0): \[ D' = (2 \times 2, 2 \times 0) = (4, 0) \]
Thus, the coordinates of the new vertices A', B', C', and D' after dilation are:
- A'(-4, -2)
- B'(-6, 4)
- C'(2, 6)
- D'(4, 0)
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