To find the coordinates of the points A', B', and C' after a dilation with a scale factor of 3 and a center of dilation at the origin, we can use the formula for dilation:
\[ (x', y') = (k \cdot x, k \cdot y) \]
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 original points:
- A(-2, -2)
- B(-4, -3)
- C(-2, -5)
We will apply the dilation to each of these points with \( k = 3 \).
For Point A(-2, -2):
\[ A' = (3 \cdot -2, 3 \cdot -2) = (-6, -6) \]
For Point B(-4, -3):
\[ B' = (3 \cdot -4, 3 \cdot -3) = (-12, -9) \]
For Point C(-2, -5):
\[ C' = (3 \cdot -2, 3 \cdot -5) = (-6, -15) \]
Summary of Transformed Points:
- \( A' = (-6, -6) \)
- \( B' = (-12, -9) \)
- \( C' = (-6, -15) \)
Thus, the coordinates of the points after dilation are:
- A'(-6, -6)
- B'(-12, -9)
- C'(-6, -15)