Question

graph line segment rs with endpoints r(2, -1) and s(6, -5) and its image after the composition of a translation along < 3, 4 > and a reflection in x = 2.

Explanation:

Step1: Perform the translation

For point $R(2,-1)$, after translation along $\langle3,4
angle$, the new - coordinates are $R'(2 + 3,-1+4)=(5,3)$. For point $S(6,-5)$, after translation along $\langle3,4
angle$, the new - coordinates are $S'(6 + 3,-5 + 4)=(9,-1)$.

Step2: Perform the reflection in the line $x = 2$

The formula for reflecting a point $(x,y)$ in the line $x=a$ is $(2a - x,y)$.
For point $R'(5,3)$ reflected in the line $x = 2$, the new coordinates are $R''(2\times2 - 5,3)=(-1,3)$.
For point $S'(9,-1)$ reflected in the line $x = 2$, the new coordinates are $S''(2\times2 - 9,-1)=(-5,-1)$.

Answer:

The endpoints of the image of line - segment $RS$ after the given composition are $R''(-1,3)$ and $S''(-5,-1)$.