To perform a dilation of a triangle with a given scale factor and center of dilation, you multiply the coordinates of each vertex by the scale factor. In this case, the center of dilation is the origin (0,0) and the scale factor is 7.
The dilation formula when the center of dilation is at the origin is: \[ (x', y') = (k \cdot x, k \cdot y) \] where \(k\) is the scale factor and \((x, y)\) are the original coordinates.
Let's apply the dilation to each vertex of triangle ABC:
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Point A(2, 1): \[ A' = (7 \cdot 2, 7 \cdot 1) = (14, 7) \]
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Point B(4, 3): \[ B' = (7 \cdot 4, 7 \cdot 3) = (28, 21) \]
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Point C(−2, 5): \[ C' = (7 \cdot -2, 7 \cdot 5) = (-14, 35) \]
Thus, the coordinates after the dilation are:
- \(A' = (14, 7)\)
- \(B' = (28, 21)\)
- \(C' = (-14, 35)\)