Find the equation of the bisector of angle A of a triangle whose vertices are A(4,3), B(0,0) and C(2,3)....
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Answers
According to angle bisector theorem,
In a triangle say ABC,
The bisector of angle A will meet at BC say at a point called X
And hence AX divides BC in the ratio AC:AB
So according to the theorem AC:AB=CX:XB
Basically from A vertex to the other 2 vertices.
In the given triangle hence,
Lets find AC:AB
We will find by distance formula.
AC=
Now find AB:
AB=
Clearly from (1) and (2) we get:
AC:AB=CX:XB
==> 2:5=CX:CB
Now according to section formula:
Let X be (x,y)
Let the ratio in which BC is divided by X be m:n
So m= 2
n = 5
x1,y1=2,3
x2,y2=0,0
==>
X=(10/7),(15/7)
Now calculate the slope of AX
x1,y1=4,3
x2,y2=(10/7,15/7)
Now this is really tiring:
y-y1=m(x-x1)
Now A = (4,3)
==> x1=4
==>y1=3
y-3=1/3(x-4)
==> 3(y-3)=x-4
==>3y-9=x-4
==>3y-x-5=0
==>x-3y+5=0
Thats the equation:
x-3y+5=0
Hope it helps!
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Answer:
According to angle bisector theorem,
In a triangle say ABC,
The bisector of angle A will meet at BC say at a point called X
And hence AX divides BC in the ratio AC:AB
So according to the theorem AC:AB=CX:XB
Basically from A vertex to the other 2 vertices.
In the given triangle hence,
Lets find AC:AB
We will find by distance formula.
AC=
Now find AB:
AB=
Clearly from (1) and (2) we get:
AC:AB=CX:XB
==> 2:5=CX:CB
Now according to section formula:
Let X be (x,y)
Let the ratio in which BC is divided by X be m:n
So m= 2
n = 5
x1,y1=2,3
x2,y2=0,0
==>
X=(10/7),(15/7)
Now calculate the slope of AX
x1,y1=4,3
x2,y2=(10/7,15/7)
Now this is really tiring:
y-y1=m(x-x1)
Now A = (4,3)
==> x1=4
==>y1=3
y-3=1/3(x-4)
==> 3(y-3)=x-4
==>3y-9=x-4
==>3y-x-5=0
==>x-3y+5=0
Thats the equation:
x-3y+5=0
Hope it helps!