Question

sometimes reflecting a point over m has the same effect as rotating the point 180° using center p. m ⊥ l 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 over a line \(m\) and a \(180^{\circ}\) rotation about a point \(P\) (where \(m\) passes through \(P\)) have the same effect for points on the line \(m\) or on the line perpendicular to \(m\) passing through \(P\).

Step2: Analyze each point

• For point \(A\): Reflecting point \(A\) over \(m\) and rotating it \(180^{\circ}\) about \(P\) gives the same image which is a point on the opposite - side of \(m\) and \(P\) at the same distance.
• For point \(B\): Since \(B\) lies on \(m\), reflecting \(B\) over \(m\) gives \(B\) itself, and rotating \(B\) \(180^{\circ}\) about \(P\) (where \(P\) is on \(m\)) also gives \(B\) itself.
• For point \(C\): The reflection of \(C\) over \(m\) and \(180^{\circ}\) rotation about \(P\) result in different locations.
• For point \(D\): The reflection of \(D\) over \(m\) and \(180^{\circ}\) rotation about \(P\) result in different locations.
• For point \(E\): Reflecting point \(E\) over \(m\) and rotating it \(180^{\circ}\) about \(P\) gives the same image which is a point on the opposite - side of \(m\) and \(P\) at the same distance.

Answer:

A. Point A
B. Point B
E. Point E