Question

lines l and m are perpendicular. sometimes reflecting a point over m has the same effect as rotating the point 180° using center p. select all labeled points which have the same image for both transformations. point a point b point c point d point e

Explanation:

Step1: Recall transformation properties

A reflection of a point over a line \(m\) and a \(180 - degree\) rotation about the intersection point \(P\) of two perpendicular lines \(l\) and \(m\) have the same effect for points on the line \(l\).

Step2: Analyze each point

• Point A: Lies on line \(l\). When reflected over \(m\) (perpendicular to \(l\) at \(P\)) and when rotated \(180^{\circ}\) about \(P\), the transformation results are the same.
• Point B: Does not lie on \(l\), so the two - transformations will give different results.
• Point C: Does not lie on \(l\), so the two - transformations will give different results.
• Point D: Does not lie on \(l\), so the two - transformations will give different results.
• Point E: Lies on line \(l\). When reflected over \(m\) (perpendicular to \(l\) at \(P\)) and when rotated \(180^{\circ}\) about \(P\), the transformation results are the same.

Answer:

A. Point A, E. Point E