Question

from unit 1 lesson 11 select all the points that stay in the same location after being reflected across line l shown here. a point a b point b c point c d point d e point e from unit 1 lesson 11 lines l and m in the following diagram are perpendicular. a point q has this property: rotating q 180° using center p has the same effect as reflecting q over line m. m ⊥ l a. give two possible locations of q. b. do all points in the plane have this property?

Explanation:

Step1: Recall reflection property

A point that stays in the same location after reflection across a line lies on the line of reflection. In the first - part, points on line \(l\) will not change position after reflection across line \(l\). Points \(B\) and \(C\) lie on line \(l\).

Step2: Analyze rotation and reflection for second - part

For a point \(Q\) such that rotating \(Q\) \(180^{\circ}\) using center \(P\) has the same effect as reflecting \(Q\) over line \(m\) (where \(m\perp l\)):

• If \(Q = P\), rotating \(Q\) \(180^{\circ}\) about \(P\) results in \(Q\) (since the center of rotation is \(P\)), and reflecting \(Q = P\) over line \(m\) (which passes through \(P\)) also results in \(Q\).
• Any point on line \(l\) has this property. When a point \(Q\) on line \(l\) is rotated \(180^{\circ}\) about \(P\), and reflected over line \(m\) (perpendicular to \(l\) through \(P\)), the results are the same.
• Not all points in the plane have this property. Points not on line \(l\) will have different results for a \(180^{\circ}\) rotation about \(P\) and a reflection over line \(m\).

Answer:

A.

1. B. Point B, C. Point C
2. a. Point \(P\) and any point on line \(l\)

b. No