Question

suppose line m is the line with the equation x = -5, line n is the line with the equation y = 1, line g is the line with the equation y = x, and line h is the line with the equation y = -2. given a(9, -3), b(6,4), and c(-1, -5), what are the coordinates of the vertices of △abc for the reflection rh? a (type an ordered pair.) b (6, -8) (type an ordered pair.) c (type an ordered pair.)

Explanation:

Step1: Reflect \( C(-1,-5) \) over \( y = -2 \)

The formula for reflecting a point \((x,y)\) over the line \(y = k\) is \((x,2k - y)\). Here \(k=-2\), \(x=-1\), \(y = -5\). So \(2k - y=2\times(-2)-(-5)=-4 + 5=1\). The \(x\) - coordinate remains the same. So \(C'=(-1,1)\)

Step2: Reflect \( A(9,-3) \) over \( y=-2 \)

Using the formula \((x,2k - y)\) with \(k = -2\), \(x = 9\), \(y=-3\). Then \(2k - y=2\times(-2)-(-3)=-4 + 3=-1\). So \(A'=(9,-1)\)

Step3: Reflect \( B(6,4) \) over \( y=-2 \)

Using the formula \((x,2k - y)\) with \(k=-2\), \(x = 6\), \(y = 4\). Then \(2k - y=2\times(-2)-4=-4-4=-8\). So \(B'=(6,-8)\)

Answer:

A. \((9,-1)\), B. \((6,-8)\), C. \((-1,1)\)