Question

reflecting a triangle
consider reflections of \\( \triangle j k l \\).
what line of reflection maps point \\( k \\) to point \\( k ^ { \prime } \\) at \\( ( - 5, \\)
2)?
\\( y \\)-axis
what line of reflection maps point \\( l \\) to point \\( l ^ { \prime } \\) at \\( ( - 2, \\)
3)?

Explanation:

Step1: Find the mid - point of \(L(-3,2)\) and \(L'(-2,3)\)

The mid - point formula is \((\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})\).
For \(x\) - coordinate: \(\frac{-3+( - 2)}{2}=\frac{-5}{2}\)
For \(y\) - coordinate: \(\frac{2 + 3}{2}=\frac{5}{2}\)

Step2: Determine the line of reflection

Since the \(x\) - coordinates of \(L\) and \(L'\) are different and the line of reflection is horizontal (because the \(x\) - coordinate of the mid - point is not relevant for a horizontal line of reflection when we consider the reflection of a point over a horizontal line). The line of reflection is \(y=\frac{y_1 + y_2}{2}\).
So the line of reflection is \(y=\frac{5}{2}\)

Answer:

\(y = \frac{5}{2}\)