Question

point f is the image when point f is reflected over the line x = -2 and then over the line y = 3. the following is the location of point f?
o a (-7,-1)
o b (-7,7)
o c (1,7)
o d (1,5)

Explanation:

Step1: Reflect over the line \(x = - 2\)

The formula for reflecting a point \((x,y)\) over the line \(x = a\) is \((2a - x,y)\). Here \(a=-2\) and the original point is \(F(-7,-1)\). So \(x\) - coordinate becomes \(2\times(-2)-(-7)=-4 + 7=3\), \(y\) - coordinate remains \(-1\). The point after reflection over \(x=-2\) is \((3,-1)\).

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

The formula for reflecting a point \((x,y)\) over the line \(y = b\) is \((x,2b - y)\). Here \(b = 3\) and the point is \((3,-1)\). So \(y\) - coordinate becomes \(2\times3-(-1)=6 + 1=7\), \(x\) - coordinate remains \(3\).

Answer:

C. \((1,7)\)