To perform a dilation of triangle ABC with a scale factor of 7 from the origin (0,0), we'll apply the formula for dilation, which is given by:
\[ (x', y') = (k \cdot x, k \cdot y) \]
where \((x, y)\) are the original coordinates, \((x', y')\) are the new coordinates after dilation, and \(k\) is the scale factor.
- 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):
\[ C' = (7 \cdot (-2), 7 \cdot 5) = (-14, 35) \]
Therefore, the coordinates of the points after dilation are:
- \(A' = (14, 7)\)
- \(B' = (28, 21)\)
- \(C' = (-14, 35)\)