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 of a triangle with a scale factor of 3 from the origin, you can use the following formula for each vertex:

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

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

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

And the scale factor \( k = 3 \), we will calculate the new coordinates:

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

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

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

So, the new coordinates after the dilation are:

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

Thus, the final answer is:

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