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Bisector of a Line

Bisector of a line is a perpendicular line which passes through the midpoint of a straight line. The bisector bisects the line at the mid point. We can find the point of the line where the perpendicular line bisects by using the mid point formula. Dividing a line into two equal segments is done by perpendicular bisector

Bisector Of a Line

In the above figure, the perpendicular bisector bisects the line segment AB at the point P. Here P is called as the midpoint of AB. The coordinates of the point P can be found with the help of the midpoint formula.

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Midpoint Formula for Bisector of a Line

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The perpendicular bisector bisects a straight line at its midpoint of the line. And so, the co ordinates of that point can be found with the help of the mid point formula.

The coordinates of the line segment AB are A(x1,y1), B(x2,y2)

Therefore, P = ((x1 + x2)/2 , (y1 + y2)/2) (Using Midpoint Formula)

Properties of Perpendicular Bisectors

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  • A line L is held to be a perpendicular bisector of a line AB if L divides AB into two equal parts at right angle. Here, C is the middle point of the line segment AB and at this point the line L intersect the line segment.
  • The line that is perpendicular to another straight line and that which bisects it is the perpendicular bisector of a line segment.
  • Perpendicular lines are intersecting each other at right angle.
  • A line or curve that bisects or divides a line segment, angle, or other build into two equal parts is called as a bisector.

Example Problems on Bisector of a Line

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Below you could see the example based on bisector of a line

Example: The perpendicular bisector bisects a straight line at its mid point. Find the mid point of the line AB. A(1,1), B(2,2)

Solution:

Given: x1=1 y1=1 x2= 2 y2=2
Formula: Mid point = ((x1 + x2)/2 , (y1 + y2)/2)

= ((1+1)/2, (2 +2)/2)

= (1,2)

The mid point at which the line bisects is (1, 2)

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