Question

given the line segment cd with coordinates c(2, -5) and d(4, 0), find the coordinates of the final image after the following glide reflection:
translation: (x, y)→(x - 3, y)
reflection: y = -1
c(
d(

Explanation:

Step1: Apply translation

For point \(C(2,-5)\):
Using the translation \((x,y)\to(x - 3,y)\), we get \(C'(2-3,-5)=(-1,-5)\)
For point \(D(4,0)\):
Using the translation \((x,y)\to(x - 3,y)\), we get \(D'(4 - 3,0)=(1,0)\)

Step2: Apply reflection \(y=-1\)

The formula for reflection over the line \(y = k\) is \((x,y)\to(x,2k - y)\). Here \(k=-1\)
For \(C'(-1,-5)\):
\(C''(-1,2\times(-1)-(-5))=(-1,-2 + 5)=(-1,3)\)
For \(D'(1,0)\):
\(D''(1,2\times(-1)-0)=(1,-2)\)

Answer:

\(C''(-1,3)\)
\(D''(1,-2)\)