To find the new triangle after applying a scale factor of 1.5 with a center of dilation at the origin, we need to multiply the coordinates of each vertex of the triangle by the scale factor.
The vertices of the original triangle are:
- \( A = (2, 2) \)
- \( B = (4, -2) \)
- \( C = (-4, -4) \)
We'll apply the scale factor of 1.5 to each vertex:
-
For vertex \( A \): \[ A' = (1.5 \times 2, 1.5 \times 2) = (3, 3) \]
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For vertex \( B \): \[ B' = (1.5 \times 4, 1.5 \times -2) = (6, -3) \]
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For vertex \( C \): \[ C' = (1.5 \times -4, 1.5 \times -4) = (-6, -6) \]
Thus, the coordinates of the new triangle after dilation are:
- \( A' = (3, 3) \)
- \( B' = (6, -3) \)
- \( C' = (-6, -6) \)
In summary, the new triangle vertices after the dilation are:
- \( A' = (3, 3) \)
- \( B' = (6, -3) \)
- \( C' = (-6, -6) \)