Question

write the coordinates of the vertices after a reflection over the line y = 3. d((□,□)) e((□,□)) f((□,□)) g((□,□))

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 \(d=\vert y - 3\vert\).
For point \(D(-5,3)\): \(d_D=\vert3 - 3\vert = 0\)
For point \(E(3,3)\): \(d_E=\vert3 - 3\vert = 0\)
For point \(F(5,8)\): \(d_F=\vert8 - 3\vert=5\)
For point \(G(-3,8)\): \(d_G=\vert8 - 3\vert = 5\)

Step2: Calculate the new \(y\) - coordinate after reflection

The formula for reflecting a point \((x,y)\) over the line \(y = a\) is \((x,2a - y)\). Here \(a = 3\), so the formula is \((x,6 - y)\)
For point \(D(-5,3)\): \(D'(-5,6 - 3)=(-5,3)\)
For point \(E(3,3)\): \(E'(3,6 - 3)=(3,3)\)
For point \(F(5,8)\): \(F'(5,6 - 8)=(5,-2)\)
For point \(G(-3,8)\): \(G'(-3,6 - 8)=(-3,-2)\)

Answer:

\(D'(-5,3)\)
\(E'(3,3)\)
\(F'(5,-2)\)
\(G'(-3,-2)\)