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: Translation

When we translate a point \((x,y)\) along the vector \(\langle a,b
angle\), the new coordinates are \((x + a,y + b)\).
For point \(R(2,-1)\): \(R'(2+3,-1 + 4)=(5,3)\)
For point \(S(6,-5)\): \(S'(6+3,-5 + 4)=(9,-1)\)

Step2: Reflection in \(x = 2\)

The formula for reflecting a point \((x,y)\) in the line \(x = c\) is \((2c-x,y)\). Here \(c = 2\).
For point \(R'(5,3)\): \(R''(2\times2 - 5,3)=(-1,3)\)
For point \(S'(9,-1)\): \(S''(2\times2 - 9,-1)=(-5,-1)\)

Answer:

Plot the original line segment \(RS\) with \(R(2,-1)\) and \(S(6,-5)\), then plot the translated - reflected line segment \(R''(-1,3)\) and \(S''(-5,-1)\)