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Question

The vertices of a triangle are A(1,7),B(5,1), and C(1,4). The equation of the bisector of ABC is ___

A
x-7y+2=0
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B
7x+y-2=0
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C
2y-7x-5=0
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D
2x+7y+5=0
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Solution

The correct option is A x-7y+2=0
Let BD be the bisector of ABC then,

AD:DC=AB:BCand AB=(5+1)2+(1+7)2=10BC=(51)2+(14)2=5AD:DC=2:1
Therefore, by section formula, D=(13,13) therefore the equation of BD is
y1=131135(x5)or y1=23143(x5)or 7y7=x5x7y+2=0

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