To find the coordinates of the vertices of triangle QRS after a translation by the vector [tex]\( T_{-7.6, 4.3} \)[/tex], let's perform the translation step-by-step for each vertex:
1. Translation of Vertex [tex]\( Q(8, -6) \)[/tex]:
- The x-coordinate of [tex]\( Q \)[/tex] is 8. After translating by [tex]\( -7.6 \)[/tex], the new x-coordinate is [tex]\( 8 + (-7.6) \)[/tex].
- The y-coordinate of [tex]\( Q \)[/tex] is -6. After translating by [tex]\( 4.3 \)[/tex], the new y-coordinate is [tex]\( -6 + 4.3 \)[/tex].
- Therefore, the coordinates of [tex]\( Q' \)[/tex] are:
[tex]\[
Q' = (8 - 7.6, -6 + 4.3) = (0.4, -1.7)
\][/tex]
2. Translation of Vertex [tex]\( R(10, 5) \)[/tex]:
- The x-coordinate of [tex]\( R \)[/tex] is 10. After translating by [tex]\( -7.6 \)[/tex], the new x-coordinate is [tex]\( 10 + (-7.6) \)[/tex].
- The y-coordinate of [tex]\( R \)[/tex] is 5. After translating by [tex]\( 4.3 \)[/tex], the new y-coordinate is [tex]\( 5 + 4.3 \)[/tex].
- Therefore, the coordinates of [tex]\( R' \)[/tex] are:
[tex]\[
R' = (10 - 7.6, 5 + 4.3) = (2.4, 9.3)
\][/tex]
3. Translation of Vertex [tex]\( S(-3, 3) \)[/tex]:
- The x-coordinate of [tex]\( S \)[/tex] is -3. After translating by [tex]\( -7.6 \)[/tex], the new x-coordinate is [tex]\( -3 + (-7.6) \)[/tex].
- The y-coordinate of [tex]\( S \)[/tex] is 3. After translating by [tex]\( 4.3 \)[/tex], the new y-coordinate is [tex]\( 3 + 4.3 \)[/tex].
- Therefore, the coordinates of [tex]\( S' \)[/tex] are:
[tex]\[
S' = (-3 - 7.6, 3 + 4.3) = (-10.6, 7.3)
\][/tex]
So, the coordinates of the vertices of the image of the triangle after the translation are:
[tex]\[
\begin{array}{l}
Q' = (0.4, -1.7) \\
R' = (2.4, 9.3) \\
S' = (-10.6, 7.3)
\end{array}
\][/tex]
