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 the points \( A' \), \( B' \), and \( C' \) after a dilation with a scale factor of 3 and with the center of dilation at the origin, we can use the formula for dilation:

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

where \( k \) is the scale factor, and \( (x, y) \) are the original coordinates of the points. Here, the scale factor \( k = 3 \).

Now we can apply this to each vertex:

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

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

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

Thus, the coordinates after dilation are:

- \( A' = (-6, -6) \)
- \( B' = (-12, -9) \)
- \( C' = (-6, -15) \)

Therefore, the final answer is:

\[
A' = (-6, -6), \quad B' = (-12, -9), \quad C' = (-6, -15)
\]