Question

Triangle ABC has vertices point A (-2, -2), point B (-4, -3), and point C (-2, -5). Find the coordinates of A' B' , and C' after a dilation with a scale factor of 3 .

Answer 1

To find the coordinates of the points A', B', and C' after a dilation with a scale factor of 3 centered at the origin (0, 0), we will use the formula for dilation:

\[
(x', y') = (k \cdot x, k \cdot y)
\]

where \(k\) is the scale factor, \(x\) and \(y\) are the original coordinates, and \(x'\) and \(y'\) are the new coordinates after dilation.

Given the scale factor \(k = 3\) and the coordinates for each point:

1. **Point A (-2, -2)**:
- \(x' = 3 \cdot (-2) = -6\)
- \(y' = 3 \cdot (-2) = -6\)
- So, \(A' = (-6, -6)\)

2. **Point B (-4, -3)**:
- \(x' = 3 \cdot (-4) = -12\)
- \(y' = 3 \cdot (-3) = -9\)
- So, \(B' = (-12, -9)\)

3. **Point C (-2, -5)**:
- \(x' = 3 \cdot (-2) = -6\)
- \(y' = 3 \cdot (-5) = -15\)
- So, \(C' = (-6, -15)\)

Thus, the coordinates after the dilation are:
- \(A' = (-6, -6)\)
- \(B' = (-12, -9)\)
- \(C' = (-6, -15)\)