Question

Triangle QRS has vertices Q(8, –6), R(10, 5), and S(–3, 3). What are the coordinates of the vertices of the image of the triangle after a translation of T–7.6, 4.3(x, y)?

Q′ =

R′ =

S′ =

Answer 1

To perform the translation \( T_{-7.6, 4.3}(x, y) \), we need to subtract 7.6 from the x-coordinates and add 4.3 to the y-coordinates of each vertex of triangle QRS.

1. **Translation for Point Q(8, -6)**:
\[
Q' = (8 - 7.6, -6 + 4.3) = (0.4, -1.7)
\]

2. **Translation for Point R(10, 5)**:
\[
R' = (10 - 7.6, 5 + 4.3) = (2.4, 9.3)
\]

3. **Translation for Point S(-3, 3)**:
\[
S' = (-3 - 7.6, 3 + 4.3) = (-10.6, 7.3)
\]

Thus, the coordinates of the vertices of the image of the triangle after the translation are:

\[
Q' = (0.4, -1.7)
\]
\[
R' = (2.4, 9.3)
\]
\[
S' = (-10.6, 7.3)
\]