Equation of Angle Bisector

Introduction :

In bisector is the separation of rather into two consequent parts, usually by a line that is then identified as bisector. The commonly consider on group of bisectors are the segment bisector and the angle bisector. Angle bisector separations the position in two angles by consequent measures. Now we study about equation of angle bisector.

Equation of Angle Bisector Definition:

The bisector of a position is the line segments to partition it in two equivalent angles on the equivalent surface as an angle. The external surface bisector of a point is line division to partition it in two equivalent angles on the different surface as an angle.

Bisector is not anything but the two lines to be bisecting to every other at the angle of 90 degree. We recognize how to bisect the line at 90 degree to make the perpendicular line by the help of compass.

Bisector is not anything but the two lines to be bisecting to every other at the angle of 90 degree

Formulas for bisectors:

Step1: slope formula with two points Formula

Slope = `((y2-y1)/(x2-x1)) ` units

Step2:The slope of the bisector

= – `(1/(slope ))`

Step 3: midpoint formula

`((x1+x2)/2)` , `((y1+y2)/2)`

Step 4: slope point type formula.

(y-y1) =m(x-x1)

Examples for Equation of Angle Bisector:

Example 1 for equation of angle bisector:

Find the equation of angle bisector, the line which passes during the points (5, 2) and (9, 6)?

Solution:

Step 1: Slope of the line= `((y2-y1)/(x2-x1))`

Step 2: (x1,y1)= (5,2)

(x2,y2)= (9, 6)

Step 3: Slope of the line = `((6-2)/ (9-5))`

= `(4/4)`

Step 4: m = 1

Step 5: slope = – `(1/ m)`

Step 6: = – `(1/1)`

Step 7: Slope of the bisector =-1

Step 8: midpoint of the line = `((x1+x2)/2)` , `((y1+y2)/2)`

= `((5+9)/2)` , `((2+6)/2)`

= `(14/2)` , `(8/2)`

Step 9: midpoint of the line segment is (7,4)

Step 10: find the equation of the bisector

Step 11: The equation is (y-y1) =m(x-x1)

Step 12: Here m is slope

(x1,y1) = (7,4)

(y- 4 ) = -1(x- 7 )

y- 4 =-x+7

x+y =7+4

x+y=11

The equation of the bisector is x+y=11

Example 2 for equation of angle bisector:

Find the equation of angle bisector, the line which passes during the points (5, 3) and (10, 8)?

Solution:

Step 1: Slope of the line= `((y2-y1)/(x2-x1))`

Step 2: (x1,y1)= (5,3)

(x2,y2)= (10, 8)

Step 3: Slope of the line = `((8-3)/ (10-5))`

= `(5/5)`

Step 4: m = 1

Step 5: slope = – `(1/ m)`

Step 6: = – `(1/1)`

Step 7: Slope of the bisector =-1

Step 8: midpoint of the line = `((x1+x2)/2)` , `((y1+y2)/2)`

= `((5+10)/2)` , `((3+8)/2)`

= `(15/2)` , `(11/2)`

Step 9: midpoint of the line segment is `(15/2)` , `(11/2)`

Step 10: find the equation of the bisector

Step 11: The equation is (y-y1) =m(x-x1)

Step 12: Here m is slope

(x1,y1) = `(15/2)` , `(11/2)`

(y- `11/2` ) = -1(x-`15/2` )

(y- `11/2` ) = -x+`15/2`

x+y = `15/2+11/2`

x+y=13

The equation of the bisector is x+y=13

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