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The vertices of a triangle are $\mathrm{A(-1,-7), B(5,1),\: and \: C(1,4)}$ . Then, the equation of the internal bisector of $\mathrm{\angle A B C}$ is

Option: 1
$\mathrm{2 x-7 y-3=0}$

Option: 2
$\mathrm{x-4 y-1=0}$

Option: 3
$\mathrm{x-7 y+2=0}$

Option: 4
$\mathrm{2 x-y-9=0}$

Answers (1)

best_answer

Using the distance formula, $\mathrm{A B=10, B C=5}$ . The internal bisector $\mathrm{B D}$ divides $\mathrm{A C}$ such that

$\mathrm{A D: D C =10: 5 }$
$\mathrm{ =2: 1 }$ (Geometrical property)

$\mathrm{\Rightarrow D}$ is $\mathrm{\left(\frac{1}{3}, \frac{1}{3}\right)}$ by section formula

Hence, the equation of $\mathrm{B D \: is\: x-7 y+2=0}$ (Two-point method).

Hence option 3 is correct.

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SANGALDEEP SINGH

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