Question

write the coordinates of the vertices after a reflection over the line $y = -1$.

Explanation:

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

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

• For \(C(3,-1)\): \(d=-1-(-1) = 0\)
• For \(D(3,7)\): \(d=7-(-1)=8\)
• For \(E(8,8)\): \(d=8-(-1)=9\)
• For \(F(8,2)\): \(d=2-(-1)=3\)

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

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

• For \(C(3,-1)\): \(x = 3\), \(y=-1\), \(C'(3,-2-(-1))=(3,-1)\)
• For \(D(3,7)\): \(x = 3\), \(y = 7\), \(D'(3,-2 - 7)=(3,-9)\)
• For \(E(8,8)\): \(x = 8\), \(y = 8\), \(E'(8,-2 - 8)=(8,-10)\)
• For \(F(8,2)\): \(x = 8\), \(y = 2\), \(F'(8,-2 - 2)=(8,-4)\)

Answer:

\(C'(3,-1)\), \(D'(3,-9)\), \(E'(8,-10)\), \(F'(8,-4)\)