Question

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 around the origin with a scale factor of 3, you multiply the coordinates of each vertex by the scale factor.

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

We will calculate the new coordinates \( A' \), \( B' \), and \( C' \) as follows:

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

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

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

Therefore, the coordinates of the dilated points are:
- \( A' = ( -6, -6 ) \)
- \( B' = ( -12, -9 ) \)
- \( C' = ( -6, -15 ) \)

So, in the required format:

A' = ([−6],[−6])
B' = ([−12],[−9])
C′ = ([−6],[−15])