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 perform a dilation with a scale factor of 3 centered at the origin for each of the points, we will multiply the coordinates of each vertex by the scale factor.

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

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

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