To find the coordinates of the vertices of triangle QRS after a translation by the vector [tex]\( T_{(-7.6, 4.3)} \)[/tex], we need to apply the translation to each vertex.
The translation vector [tex]\( T_{(-7.6, 4.3)} \)[/tex] tells us to shift the coordinates of each vertex by -7.6 units in the x-direction and 4.3 units in the y-direction.
Let's go through each vertex one by one:
1. Vertex Q: (8, -6)
- To translate Q by [tex]\((-7.6, 4.3)\)[/tex], we add -7.6 to the x-coordinate and 4.3 to the y-coordinate of Q:
[tex]\[
Q^{\prime} = (8 + (-7.6), -6 + 4.3)
\][/tex]
Simplifying this, we get:
[tex]\[
Q^{\prime} = (0.4, -1.7)
\][/tex]
2. Vertex R: (10, 5)
- To translate R by [tex]\((-7.6, 4.3)\)[/tex], we add -7.6 to the x-coordinate and 4.3 to the y-coordinate of R:
[tex]\[
R^{\prime} = (10 + (-7.6), 5 + 4.3)
\][/tex]
Simplifying this, we get:
[tex]\[
R^{\prime} = (2.4, 9.3)
\][/tex]
3. Vertex S: (-3, 3)
- To translate S by [tex]\((-7.6, 4.3)\)[/tex], we add -7.6 to the x-coordinate and 4.3 to the y-coordinate of S:
[tex]\[
S^{\prime} = (-3 + (-7.6), 3 + 4.3)
\][/tex]
Simplifying this, we get:
[tex]\[
S^{\prime} = (-10.6, 7.3)
\][/tex]
Therefore, the coordinates of the vertices of the image of triangle QRS after the translation are:
[tex]\[
Q^{\prime} = (0.4, -1.7)
\][/tex]
[tex]\[
R^{\prime} = (2.4, 9.3)
\][/tex]
[tex]\[
S^{\prime} = (-10.6, 7.3)
\][/tex]
