Question

write the coordinates of the vertices after a reflection over the line x = -5.

Explanation:

Step1: Identify original coordinates

Let's assume the coordinates of the vertices are \(C(-4, - 1)\), \(D(-2,-1)\), \(E(-2,0)\), \(F(-4,0)\)

Step2: Use reflection formula for \(x = a\)

The formula for reflecting a point \((x,y)\) over the line \(x = a\) is \((2a - x,y)\). Here \(a=-5\).
For point \(C(-4,-1)\):
\[2\times(-5)-(-4)=-10 + 4=-6\]
The new - coordinate is \(C'(-6,-1)\)
For point \(D(-2,-1)\):
\[2\times(-5)-(-2)=-10 + 2=-8\]
The new - coordinate is \(D'(-8,-1)\)
For point \(E(-2,0)\):
\[2\times(-5)-(-2)=-10 + 2=-8\]
The new - coordinate is \(E'(-8,0)\)
For point \(F(-4,0)\):
\[2\times(-5)-(-4)=-10 + 4=-6\]
The new - coordinate is \(F'(-6,0)\)

Answer:

\(C'(-6,-1)\), \(D'(-8,-1)\), \(E'(-8,0)\), \(F'(-6,0)\)