To dilate a triangle (or any figure) from the origin with a scale factor (magnitude) of 3, you multiply the coordinates of each vertex by the scale factor.
The original vertices of the triangle are:
- A(-2, -5)
- B(0, 3)
- C(6, -3)
Now, applying the dilation with a scale factor of 3:
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For vertex A: \[ A' = (3 \times -2, 3 \times -5) = (-6, -15) \]
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For vertex B: \[ B' = (3 \times 0, 3 \times 3) = (0, 9) \]
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For vertex C: \[ C' = (3 \times 6, 3 \times -3) = (18, -9) \]
Thus, the coordinates of the new vertices after the dilation are:
- A'(-6, -15)
- B'(0, 9)
- C'(18, -9)
So, the new vertices of triangle A'B'C' are:
- A'(-6, -15)
- B'(0, 9)
- C'(18, -9)
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