Question

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

Explanation:

Step1: Recall the rule for reflection over x = a

For a point \((x,y)\) reflected over the line \(x = a\), the new \(x\)-coordinate is \(2a - x\) and the \(y\)-coordinate remains the same. Here \(a = 1\).

Step2: Find \(K'\)

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

Step3: Find \(L'\)

The coordinates of \(L\) are \((8,-1)\). Using the formula \(x'=2\times1 - 8=-6\), \(y'=-1\). So \(L'(-6,-1)\)

Step4: Find \(M'\)

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

Step5: Find \(N'\)

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

Answer:

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