Question

write the coordinates of the vertices after a reflection over the line x = 2.

Explanation:

Step1: Identify original coordinates

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

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 \(a = 2\).
For point \(C(0,-2)\):
\(x'=2\times2 - 0=4\), \(y'=-2\), so the new - coordinate is \(C'(4,-2)\)
For point \(D(2,-2)\):
\(x'=2\times2 - 2 = 2\), \(y'=-2\), so the new - coordinate is \(D'(2,-2)\)
For point \(E(0,2)\):
\(x'=2\times2 - 0=4\), \(y'=2\), so the new - coordinate is \(E'(4,2)\)
For point \(F(-2,-2)\):
\(x'=2\times2-(-2)=6\), \(y'=-2\), so the new - coordinate is \(F'(6,-2)\)

Answer:

The coordinates of the vertices after reflection over the line \(x = 2\) are \(C'(4,-2)\), \(D'(2,-2)\), \(E'(4,2)\), \(F'(6,-2)\)