To find the coordinates \(A'\) and \(B'\) after dilation of points \(A\) and \(B\) with a scale factor of 13 centered at the origin, we use the dilation transformation formula:
\[ (x, y) \rightarrow (kx, ky) \]
where \(k\) is the scale factor.
Given:
- \(A(-6, 3)\)
- \(B(-12, 9)\)
- Scale factor \(k = 13\)
Now we apply the dilation to each point:
For point \(A(-6, 3)\):
\[ A' = (13 \cdot -6, 13 \cdot 3) = (-78, 39) \]
For point \(B(-12, 9)\):
\[ B' = (13 \cdot -12, 13 \cdot 9) = (-156, 117) \]
Thus, the coordinates after dilation are:
- \(A'(-78, 39)\)
- \(B'(-156, 117)\)
In summary:
- \(A' = (-78, 39)\)
- \(B' = (-156, 117)\)
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