Question

write the coordinates of the vertices after a reflection over the line ( y = -4 ).

Explanation:

Step1: Recall the rule for reflection over a horizontal line

When reflecting a point \((x,y)\) over the line \(y = k\), the formula is \((x,2k - y)\). Here \(k=-4\), so the formula becomes \((x,2\times(-4)-y)=(x,-8 - y)\)

Step2: Find the coordinates of \(C\)

The coordinates of \(C\) are \((8,-4)\). Using the formula \((x,-8 - y)\), substitute \(x = 8\) and \(y=-4\). Then \(C'=(8,-8-(-4))=(8,-4)\)

Step3: Find the coordinates of \(D\)

The coordinates of \(D\) are \((9,-4)\). Using the formula \((x,-8 - y)\), substitute \(x = 9\) and \(y = -4\). Then \(D'=(9,-8-(-4))=(9,-4)\)

Step4: Find the coordinates of \(E\)

The coordinates of \(E\) are \((9,1)\). Using the formula \((x,-8 - y)\), substitute \(x = 9\) and \(y = 1\). Then \(E'=(9,-8 - 1)=(9,-9)\)

Step5: Find the coordinates of \(F\)

The coordinates of \(F\) are \((8,1)\). Using the formula \((x,-8 - y)\), substitute \(x = 8\) and \(y = 1\). Then \(F'=(8,-8 - 1)=(8,-9)\)

Answer:

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