Question

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

Explanation:

Step1: Reflect about \(x = 6\)

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

Step2: Reflect \((11,2)\) about \(x = 4\)

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

Answer:

\(-3\)