Question

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

Explanation:

Step1: Recall transformation properties

For a point - reflection over a point (center of rotation) and a line - reflection over a line perpendicular to the first - line passing through the center of rotation, we know that for points on the line of symmetry (in this case, the intersection of the two perpendicular lines \(l\) and \(m\) at point \(P\)), the two transformations (reflection over \(m\) and rotation of 180 degrees about \(P\)) have the same effect.

Step2: Analyze the position of points

Points \(A\) and \(E\) are on the line \(l\), and points \(B\) is on the line \(m\). When we reflect a point on the line of reflection \(m\) over \(m\), the point remains in the same position. When we rotate a point on the line passing through the center of rotation \(P\) (in this case, \(l\) and \(m\) intersect at \(P\)) 180 degrees about \(P\), points on the lines \(l\) and \(m\) will have the same image for the two transformations.

Answer:

A. A, B, E