How do you find the equation of a perpendicular bisector of a line segment?

Perpendicular bisector will pass through the points A and B i.e. point M. In this case, the perpendicular bisector is eventually a line passing through point M(5,3) and having slope m2=1. Thus the equation of the perpendicular bisector is x−y−2=0.

What is a line perpendicular to a given line segment that passes through the line segments midpoint?

A bisector of a line segment will pass through the midpoint of the line segment. A perpendicular bisector of a segment passes through the midpoint of the line segment and is perpendicular to the line segment.

What is perpendicular bisector of a line?

A perpendicular bisector of a line segment is a line segment perpendicular to and passing through the midpoint of (left figure). The perpendicular bisector of a line segment can be constructed using a compass by drawing circles centered at and with radius and connecting their two intersections.

How do you write an equation for a perpendicular line?

Perpendicular lines have opposite-reciprocal slopes, so the slope of the line we want to find is 1/2. Plugging in the point given into the equation y = 1/2x + b and solving for b, we get b = 6. Thus, the equation of the line is y = ½x + 6.

How do you find the equation of the line perpendicular and passing through the midpoint?

1 Answer

1. The midpoint is (x1+x22,y1+y22).
2. The slope of ¯PQ is m=y2−y1x2−x1, so the slope of a perpendicular is −1m=x1−x2y2−y1.
3. Finally, the equation of the perpendicular bisector of ¯PQ is then y−y1+y22=x1−x2y2−y1(x−x1+x22).

Which of the following information is needed to determine the equation of the perpendicular bisector of a line segment?

First, you must find the midpoint of the segment, the formula for which is (x1+x22,y1+y22) . This gives (−5,3) as the midpoint. This is the point at which the segment will be bisected. Next, since we are finding a perpendicular bisector, we must determine what slope is perpendicular to that of the existing segment.

What is perpendicular bisector triangle?

The perpendicular bisector of a side of a triangle is a line perpendicular to the side and passing through its midpoint. The three perpendicular bisectors of the sides of a triangle meet in a single point, called the circumcenter . A point where three or more lines intersect is called a point of concurrency.