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 and a center point of dilation at the origin. (2 points)

A' = (___,___)

B' = (___,___)

C' = (___,___)

Answer 1

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.

1. **Dilation of point A (-2, -2)**:
\[
A' = (3 \cdot -2, 3 \cdot -2) = (-6, -6)
\]

2. **Dilation of point B (-4, -3)**:
\[
B' = (3 \cdot -4, 3 \cdot -3) = (-12, -9)
\]

3. **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)