Question

write the coordinates of the vertices after a reflection over the line ( x = - 3 ).

Explanation:

Step1: Recall the reflection formula

For a point \((x,y)\) reflected over the line \(x = a\), the formula is \((2a - x,y)\). Here \(a=-3\).

Step2: Find the coordinates of \(K\)

The original coordinate of \(K\) is \((0,0)\). Using the formula \(x'=2\times(-3)-0=-6\), \(y' = 0\). So \(K'(-6,0)\).

Step3: Find the coordinates of \(L\)

The original coordinate of \(L\) is \((-1,4)\). Using the formula \(x'=2\times(-3)-(-1)=-6 + 1=-5\), \(y'=4\). So \(L'(-5,4)\).

Step4: Find the coordinates of \(M\)

The original coordinate of \(M\) is \((1,4)\). Using the formula \(x'=2\times(-3)-1=-6-1=-7\), \(y' = 4\). So \(M'(-7,4)\).

Step5: Find the coordinates of \(N\)

The original coordinate of \(N\) is \((2,0)\). Using the formula \(x'=2\times(-3)-2=-6 - 2=-8\), \(y'=0\). So \(N'(-8,0)\).

Answer:

\(K'(-6,0)\), \(L'(-5,4)\), \(M'(-7,4)\), \(N'(-8,0)\)