To find the coordinates of points A', B', and C' after a dilation with a scale factor of 3 from the origin, we can use the formula for dilation:
\[ (x', y') = (k \cdot x, k \cdot y) \]
where \((x, y)\) are the original coordinates, \(k\) is the scale factor, and \((x', y')\) are the new coordinates after dilation.
Given points:
- A (-2, -2)
- B (-4, -3)
- C (-2, -5)
We will apply the dilation for each point.
-
Dilation of point A (-2, -2): \[ A' = (3 \cdot -2, 3 \cdot -2) = (-6, -6) \]
-
Dilation of point B (-4, -3): \[ B' = (3 \cdot -4, 3 \cdot -3) = (-12, -9) \]
-
Dilation of point C (-2, -5): \[ C' = (3 \cdot -2, 3 \cdot -5) = (-6, -15) \]
Now, we can summarize the new coordinates:
- A' = (-6, -6)
- B' = (-12, -9)
- C' = (-6, -15)
Thus, the final answers are:
A' = (-6, -6)
B' = (-12, -9)
C' = (-6, -15)