Question

write the coordinates of the vertices after a reflection over the line $x = 1$.

Explanation:

Step1: Recall the reflection formula

For a reflection over the line \(x = a\), the formula for the \(x\)-coordinate of a point \((x,y)\) is \(x'=2a - x\), and the \(y\)-coordinate remains the same (\(y'=y\)). Here \(a = 1\).

Step2: Find the new \(x\)-coordinate for each point

• For point \(K(3,-1)\):

\(x'=2\times1 - 3=2 - 3=-1\), \(y'=-1\). So the new coordinate is \((-1,-1)\)

• For point \(N(3,6)\):

\(x'=2\times1 - 3=2 - 3=-1\), \(y' = 6\). So the new coordinate is \((-1,6)\)

• For point \(M(8,6)\):

\(x'=2\times1 - 8=2 - 8=-6\), \(y' = 6\). So the new coordinate is \((-6,6)\)

• For point \(L(8,-1)\):

\(x'=2\times1 - 8=2 - 8=-6\), \(y'=-1\). So the new coordinate is \((-6,-1)\)

Answer:

\(K'(-1,-1)\), \(N'(-1,6)\), \(M'(-6,6)\), \(L'(-6,-1)\)