Question

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

Explanation:

Step1: Recall the reflection formula

For a point \((x,y)\) reflected over the line \(x = a\), the formula is \((2a - x,y)\). Here \(a = 1\).

Step2: Find the coordinates of \(K\)

The original coordinates of \(K\) are \((3,0)\). Using the formula \(x'=2\times1 - 3=-1\), \(y' = 0\). So the new coordinates are \((-1,0)\).

Step3: Find the coordinates of \(N\)

The original coordinates of \(N\) are \((3,6)\). Using the formula \(x'=2\times1 - 3=-1\), \(y' = 6\). So the new coordinates are \((-1,6)\).

Step4: Find the coordinates of \(L\)

The original coordinates of \(L\) are \((8,0)\). Using the formula \(x'=2\times1 - 8=-6\), \(y' = 0\). So the new coordinates are \((-6,0)\).

Step5: Find the coordinates of \(M\)

The original coordinates of \(M\) are \((8,6)\). Using the formula \(x'=2\times1 - 8=-6\), \(y' = 6\). So the new coordinates are \((-6,6)\).

Answer:

\(K'(-1,0)\), \(N'(-1,6)\), \(L'(-6,0)\), \(M'(-6,6)\)