Question

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

Explanation:

Step1: Find the distance from each point to the line \(x = 1\)

For a point \((x,y)\), the distance to the line \(x = 1\) is \(|x - 1|\).

• For \(K(3,0)\), distance \(d=|3 - 1|=2\)
• For \(L(8,0)\), distance \(d = |8 - 1|=7\)
• For \(M(8,6)\), distance \(d=|8 - 1|=7\)
• For \(N(3,6)\), distance \(d=|3 - 1|=2\)

Step2: Calculate the new \(x\) - coordinate

The formula for reflecting a point \((x,y)\) over the line \(x = a\) is \((2a - x,y)\). Here \(a = 1\), so the formula is \((2\times1 - x,y)=(2 - x,y)\)

• For \(K(3,0)\): \(x'=2-3=-1\), \(y' = 0\), so \(K'(-1,0)\)
• For \(L(8,0)\): \(x'=2 - 8=-6\), \(y'=0\), so \(L'(-6,0)\)
• For \(M(8,6)\): \(x'=2 - 8=-6\), \(y'=6\), so \(M'(-6,6)\)
• For \(N(3,6)\): \(x'=2 - 3=-1\), \(y'=6\), so \(N'(-1,6)\)

Answer:

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