Certainly! To find the coordinates of the vertices of triangle [tex]\(QRS\)[/tex] after a translation by the vector [tex]\( T(-7.6, 4.3) \)[/tex], we will perform the translation operation on each vertex.
### Step-by-Step Solution
1. Identify the original coordinates of the vertices:
- [tex]\( Q(8, -6) \)[/tex]
- [tex]\( R(10, 5) \)[/tex]
- [tex]\( S(-3, 3) \)[/tex]
2. Translation vector:
- The translation vector is [tex]\(T(-7.6, 4.3)\)[/tex].
3. Translation operation:
- To translate a point [tex]\((x, y)\)[/tex] by [tex]\((a, b)\)[/tex], we add [tex]\(a\)[/tex] to the [tex]\(x\)[/tex]-coordinate and [tex]\(b\)[/tex] to the [tex]\(y\)[/tex]-coordinate.
4. Translate each vertex:
- For vertex [tex]\(Q(8, -6)\)[/tex]:
[tex]\[
Q' = (8 + (-7.6), -6 + 4.3) = (0.4, -1.7)
\][/tex]
- For vertex [tex]\(R(10, 5)\)[/tex]:
[tex]\[
R' = (10 + (-7.6), 5 + 4.3) = (2.4, 9.3)
\][/tex]
- For vertex [tex]\(S(-3, 3)\)[/tex]:
[tex]\[
S' = (-3 + (-7.6), 3 + 4.3) = (-10.6, 7.3)
\][/tex]
### Result
Thus, the coordinates of the vertices after the translation are:
[tex]\[
\begin{array}{l}
Q' = (0.4, -1.7) \checkmark \\
R' = (2.4, 9.3) \checkmark \\
S' = (-10.6, 7.3)
\end{array}
\][/tex]
