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

Answer 1

To find the coordinates of the points \( A' \), \( B' \), and \( C' \) after a dilation with a scale factor of 3 and the center of dilation at the origin, we can use the formula for dilation. The formula for the coordinates of a point \( (x, y) \) after a dilation from the origin by a scale factor \( k \) is:

\[
(x', y') = (kx, ky)
\]

Given the vertices of triangle \( ABC \):
- Point \( A(-2, -2) \)
- Point \( B(-4, -3) \)
- Point \( C(-2, -5) \)

Let's calculate the new coordinates.

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

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

3. For point \( C(-2, -5) \):
\[
C' = (3 \cdot -2, 3 \cdot -5) = (-6, -15)
\]

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

So, the final answer is:
- \( A' = (-6, -6) \)
- \( B' = (-12, -9) \)
- \( C' = (-6, -15) \)