To find the coordinates of the points A′, B′, and C′ after dilation with a scale factor of 7 and the center of dilation at the origin (0,0), we can use the following formula for dilation:
\[ (x', y') = (kx, ky) \]
where \( (x, y) \) are the original coordinates of the point, \( k \) is the scale factor, and \( (x', y') \) are the new coordinates after dilation.
Given the scale factor \( k = 7 \), we can find:
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For point A(2, 1): \[ A' = (7 \times 2, 7 \times 1) = (14, 7) \]
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For point B(4, 3): \[ B' = (7 \times 4, 7 \times 3) = (28, 21) \]
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For point C(−2, 5): \[ C' = (7 \times (-2), 7 \times 5) = (-14, 35) \]
Thus, the coordinates of the points after dilation are:
- \( A' (14, 7) \)
- \( B' (28, 21) \)
- \( C' (-14, 35) \)
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