Question

6 from unit 1, lesson 11 lines l and m are perpendicular. 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 a point a b point b c point c d point d e point e

Explanation:

Step1: Recall reflection and rotation properties

A reflection over line $m$ and a $180^{\circ}$ rotation about point $P$ (where $m\perp l$ and they intersect at $P$) will have the same result for points on line $m$ and line $l$.

Step2: Analyze each point

• Point $A$: On line $l$. Reflecting over $m$ and rotating $180^{\circ}$ about $P$ gives the same image.
• Point $B$: On line $m$. Reflecting over $m$ (it maps to itself) and rotating $180^{\circ}$ about $P$ gives the same result (itself).
• Point $C$: Not on $m$ or $l$, so the two transformations will give different images.
• Point $D$: Not on $m$ or $l$, so the two transformations will give different images.
• Point $E$: On line $l$. Reflecting over $m$ and rotating $180^{\circ}$ about $P$ gives the same image.

Answer:

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