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The vertices of a triangle are (A(-1,-7)...

The vertices of a triangle are `(A(-1,-7),B(5,1),` and `C(1,4)dot` The equation of the bisector of `/_A B C` is____

Text Solution

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Equation of the line `AB` is `y-1=(1-(-7))/(5-(-1))(x-5)`
`impliesy-1=(8)/(6)(x-5)impliesy-1)=(4)/(3)(x-5)`
`implies3y-3=4x-20`
`implies3y-4x+17=0`
Equation of the line `BC` is
`y-4=(4-1)/(1-5)(x-1)impliesy-4=-(3)/(4)(x-1)`
`implies4y-16=-3x+3implies3x+4y-19=0`
Again, equation of the bisectors of the angles between two given lines `AB` and `BC` are
`(3y-4x+17)/(sqrt(3^(2)+4^(2)))=+-(4y+3x-19)/(sqrt(4^(2)+3^(2)))`
`implies3y-4x+17=+-(4y+3x-19)`
`implies3y-4x+17=4y+3x-19`
and `3y-4x+17=-(4y+3x-19)`
`implies36=y+7x` and `7y-x=2`
Out of these two, equation of the bisector of angle `ABC` is
`7y=x+2`
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