To find the coordinates of the new triangle [tex]\( A'B'C' \)[/tex] after dilation, we need to apply the given scale factor to each vertex of the original triangle [tex]\( ABC \)[/tex].
The vertices of triangle [tex]\( ABC \)[/tex] are:
- [tex]\( A(2, 2) \)[/tex]
- [tex]\( B(4, 2) \)[/tex]
- [tex]\( C(4, 3) \)[/tex]
The dilation factor is 2, so we multiply each coordinate by 2:
1. For [tex]\( A \)[/tex]:
[tex]\[
A' = (2 \cdot 2, 2 \cdot 2) = (4, 4)
\][/tex]
2. For [tex]\( B \)[/tex]:
[tex]\[
B' = (4 \cdot 2, 2 \cdot 2) = (8, 4)
\][/tex]
3. For [tex]\( C \)[/tex]:
[tex]\[
C' = (4 \cdot 2, 3 \cdot 2) = (8, 6)
\][/tex]
So, the coordinates of [tex]\( A', B', \)[/tex] and [tex]\( C' \)[/tex] after dilation are:
- [tex]\( A'(4, 4) \)[/tex]
- [tex]\( B'(8, 4) \)[/tex]
- [tex]\( C'(8, 6) \)[/tex]
Given the multiple choice options, the correct answer is:
B [tex]\( \quad A^{\prime}(4,4), B^{\prime}(8,4), C^{\prime}(8,6) \)[/tex]
