To find the new coordinates of vertex A' after dilating the point A at (-1, 3) from the origin with a scale factor of 3, you can use the following formula for dilation:
\[ A' = (kx, ky) \]
where \( k \) is the scale factor, and \( (x, y) \) are the original coordinates.
For vertex A at (-1, 3):
- \( k = 3 \)
- Original coordinates \( (x, y) = (-1, 3) \)
Now apply the formula:
\[ A' = (3 \cdot -1, 3 \cdot 3) = (-3, 9) \]
Thus, the new coordinates of vertex A' after dilation are \( (-3, 9) \).
You can apply the same process to find the new coordinates of the other vertices B, C, and D if desired.
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For B(2, 6): \[ B' = (3 \cdot 2, 3 \cdot 6) = (6, 18) \]
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For C(5, 2): \[ C' = (3 \cdot 5, 3 \cdot 2) = (15, 6) \]
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For D(1, 1): \[ D' = (3 \cdot 1, 3 \cdot 1) = (3, 3) \]
Thus, the new coordinates after dilation will be:
- \( A' = (-3, 9) \)
- \( B' = (6, 18) \)
- \( C' = (15, 6) \)
- \( D' = (3, 3) \)