# Perpendicular Bisector: Understanding the Wording

• MHB
• Yazan975
In summary, a perpendicular bisector is a line or line segment that intersects another line segment at a 90 degree angle, cutting it into two equal parts. To find the perpendicular bisector, you need to first locate the midpoint and then draw arcs on either side of it, intersecting the endpoints of the line segment. Understanding the wording of "perpendicular bisector" is important as it helps with identification and construction. It is related to other geometric concepts such as perpendicular lines and symmetry. A perpendicular bisector can be constructed for any line segment using a compass and the midpoint.
Yazan975
View attachment 8416

I know that when two lines are perpendicular their gradients multiply to -1 but I don't get the wording here.
Any suggestions?

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The line through (1, 2) and (-5, -4) has slope $\frac{-5- 1}{-4- 2}= \frac{-6}{6}= 1$ so any line perpendicular to that has slope -1. Further the perpendicular **bisector** goes through the point exactly half way between (1, 2) and (-5, 4) which is $\left(\frac{1+ (-5)}{2}, \frac{2+ 4}{2}\right)$$= \left(\frac{-4}{2},\frac{6}{3}\right)= (-2, 3)$.

What is the equation of the line through (-2, 3) with slope -1?

## 1. What is a perpendicular bisector?

A perpendicular bisector is a line or line segment that intersects another line segment at a 90 degree angle, cutting it into two equal parts.

## 2. How do you find the perpendicular bisector of a line segment?

To find the perpendicular bisector of a line segment, you need to first locate the midpoint of the line segment. Then, using a compass, draw arcs on either side of the midpoint, making sure they intersect the endpoints of the line segment. Finally, draw a straight line through the midpoint and the intersection points of the arcs, and this line will be the perpendicular bisector.

## 3. Why is it important to understand the wording of "perpendicular bisector"?

Understanding the wording of "perpendicular bisector" is important because it can help you accurately identify and construct this geometric concept. It also helps to clarify the relationship between the bisector and the original line segment.

## 4. How does a perpendicular bisector relate to other geometric concepts?

A perpendicular bisector is related to other geometric concepts such as perpendicular lines, which are two lines that intersect at a 90 degree angle. It is also related to symmetry, as the perpendicular bisector divides a line segment into two equal parts, creating symmetry.

## 5. Can a perpendicular bisector be constructed for any line segment?

Yes, a perpendicular bisector can be constructed for any line segment, regardless of its length or position. As long as you can locate the midpoint and use a compass, you can construct a perpendicular bisector for any line segment.

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