To perform a dilation of a point with respect to a center of dilation and a scale factor, we can use the following formula:
\[ (x', y') = (kx, ky) \]
where \((x, y)\) are the original coordinates of the point, \(k\) is the scale factor, and \((x', y')\) are the coordinates after dilation.
In this case, the center of dilation is at the origin \((0, 0)\), and the scale factor \(k\) is 4.
We will find the coordinates of points A', B', and C' after dilation.
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For point A (-3, -3): \[ A' = (4 \cdot -3, 4 \cdot -3) = (-12, -12) \]
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For point B (-5, -4): \[ B' = (4 \cdot -5, 4 \cdot -4) = (-20, -16) \]
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For point C (-3, -5): \[ C' = (4 \cdot -3, 4 \cdot -5) = (-12, -20) \]
Now we have the coordinates after dilation:
- \( A' = (-12, -12) \)
- \( B' = (-20, -16) \)
- \( C' = (-12, -20) \)
Thus, the coordinates of A', B', and C' after the dilation are:
- \( A' = (-12, -12) \)
- \( B' = (-20, -16) \)
- \( C' = (-12, -20) \)
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