Question

if p = (3,4), find: r_{y = 5}(p) (?, )

Explanation:

Step1: Determine the rule for reflection over the line \(y = 5\)

When reflecting a point \((x,y)\) over the line \(y = k\), the \(x -\)coordinate remains the same, and the formula for the \(y -\)coordinate is \(y'=2k - y\). Here \(k = 5\) and the point \(P=(x,y)=(3,4)\).

Step2: Calculate the \(y -\)coordinate of the reflected point

For the \(x -\)coordinate: \(x'=x = 3\) (since reflection over a horizontal line does not change the \(x -\)value).
For the \(y -\)coordinate: use the formula \(y'=2k - y\). Substitute \(k = 5\) and \(y = 4\) into the formula. Then \(y'=2\times5-4=10 - 4=6\).

Answer:

\((3,6)\)