Question

find the image of (1,2) after a reflection about x = 6 followed by a reflection about x = 4. (-3, ?) enter the number that belongs in the green box.

Explanation:

Step1: Reflection about \(x = 6\)

The formula for reflection of a point \((x,y)\) about the line \(x = a\) is \((2a - x,y)\).
For the point \((1,2)\) and \(a = 6\), we have \(x'=2\times6 - 1=11\), \(y' = 2\). So the image is \((11,2)\).

Step2: Reflection about \(x = 4\)

Using the formula \((x,y)\to(2a - x,y)\) again, with \(a = 4\) and the point \((11,2)\).
We calculate \(x''=2\times4 - 11=-3\), \(y'' = 2\).

Answer:

\(2\)