Question

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

( c(square,square) )

( d(square,square) )

( e(square,square) )

( f(square,square) )

Explanation:

Step1: Find the distance from each point to the line \(y = 3\)

For a point \((x,y)\), the distance to the line \(y = 3\) is \(d=|y - 3|\).

• For point \(C(-7, - 1)\): \(d=|-1 - 3|=4\)
• For point \(D(-2,-1)\): \(d=|-1 - 3|=4\)
• For point \(E(-5,1)\): \(d=|1 - 3|=2\)
• For point \(F(-6,1)\): \(d=|1 - 3|=2\)

Step2: Reflect the points over the line \(y = 3\)

When reflecting a point \((x,y)\) over the line \(y = 3\), the \(x\)-coordinate remains the same, and the \(y\)-coordinate is \(y'=3+(3 - y)\)

• For \(C(-7,-1)\): \(y'=3+(3-(-1))=3 + 4=7\), so \(C'(-7,7)\)
• For \(D(-2,-1)\): \(y'=3+(3-(-1))=3 + 4=7\), so \(D'(-2,7)\)
• For \(E(-5,1)\): \(y'=3+(3 - 1)=3+2=5\), so \(E'(-5,5)\)
• For \(F(-6,1)\): \(y'=3+(3 - 1)=3+2=5\), so \(F'(-6,5)\)

Answer:

\(C'(-7,7)\), \(D'(-2,7)\), \(E'(-5,5)\), \(F'(-6,5)\)