To find the coordinates of the points \( A' \), \( B' \), and \( C' \) after dilation with a scale factor of 7 and a center point of dilation at the origin (0,0), we use the formula for dilation:
\[ A' = k \cdot (x_A, y_A) \] where \( k \) is the scale factor and \( (x_A, y_A) \) are the original coordinates of the point.
Applying this to each vertex:
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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 \( C(-2,5) \): \[ C' = (7 \cdot -2, 7 \cdot 5) = (-14, 35) \]
So, the coordinates of the points after dilation are:
- \( A' = (14, 7) \)
- \( B' = (28, 21) \)
- \( C' = (-14, 35) \)
Thus, the final answers are:
\[ A' = (14, 7) \] \[ B' = (28, 21) \] \[ C' = (-14, 35) \]
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