Question

1. esteban said ( r_{n}(abc)\to(abc) ), where the equation of line ( n ) is ( x = 4 ), is the rule for the reflection. what was his error?

Explanation:

Step1: Recall reflection rule

For a reflection over the line \(x = a\), the rule is \((x,y)\to(2a - x,y)\).

Step2: Check the line of reflection

Esteban said the line of reflection is \(x = 4\). But if we check the coordinates of the points (for example, if \(A=(1,5)\) and \(A'=(1,3)\), the mid - point of \(A\) and \(A'\) is \((1,4)\), which implies reflection over \(y = 4\) (not \(x = 4\)). The general formula for reflection over \(y = k\) is \((x,y)\to(x,2k - y)\).

Answer:

Esteban's error was that the line of reflection is \(y = 4\) (not \(x = 4\)).