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