To perform a dilation of a triangle with a scale factor of \( k \) and a center of dilation at the origin (0, 0), you can use the following formula for the coordinates of the dilated points:
\[ (x', y') = (k \cdot x, k \cdot y) \]
In this case, the scale factor \( k \) is 7. Now we will apply this formula to each vertex of triangle ABC:
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For point A(2, 1): \[ A' = (7 \cdot 2, 7 \cdot 1) = (14, 7) \]
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For point B(4, 3): \[ B' = (7 \cdot 4, 7 \cdot 3) = (28, 21) \]
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For point C(−2, 5): \[ C' = (7 \cdot (-2), 7 \cdot 5) = (-14, 35) \]
Thus, the coordinates after the dilation are:
- \( A' = (14, 7) \)
- \( B' = (28, 21) \)
- \( C' = (-14, 35) \)
So, the final answers are:
- \( A' = (14, 7) \)
- \( B' = (28, 21) \)
- \( C' = (-14, 35) \)