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