Question

Janie uses a reflecting tool to reflect Point B onto Point A. Which of the following statements are true about the line of reflection?
1. Reflection line is perpendicular to AB
2. Reflection line does not bisect AB.
3. Reflection line passes through the midpoint of BA.
4. Reflection line forms two equal angles with segment AB.

Answer 1

Hello,

1:TRUE
2:FALSE
3:TRUE
4:TRUE

Answer 2

You can understand the concept of reflection by imagining a lake. Suppose a mountain is reflected on the lake across an imaginary horizontal line in the ground. This line is the Line of Symmetry. So, in this problem we need to solve four items. Therefore:

1. Reflection line is perpendicular to AB

This is true. To reflect Point B onto Point A, we need to take a Line of Symmetry perpendicular to the segment AB as illustrated in Figure 1. This line is the one in red and the blue square indicates that the red line and the segment AB are perpendicular.  

2. Reflection line does not bisect AB

This is false. Instead, the line in red bisect the segment AB, that is, it divides the segment into two equal parts as indicated in Figure 2. The x in blue represents the point at which the red line bisects the segment.

3.  Reflection line passes through the midpoint of BA.

This is true. Given that the red line divide the segment into two equal parts, then the point at which the red line bisects the segment is also called the midpoint (M) as indicated in Figure 3.

4. Reflection line forms two equal angles with segment AB.

This is true. As you can see in Figure 4, the two blue angles are equal and the two green angles are equal. So, reflection line forms two equal angles with segment AB. In fact, each of these angles measures 90 degrees. Accordingly, all these four angles are equal.