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
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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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)
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)
Given: x1=1 y1=1 x2= 2 y2=2
Formula: Mid point = ((x1 + x2)/2 , (y1 + y2)/2)
= ((1+1)/2, (2 +2)/2)
The mid point at which the line bisects is (1, 2)
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