Question

The equation of the internal bisector of angle BAC of the triangle ABC whose vertices are $A(5,2),B(2,3),C(6,5)$ is

• A. $6x+y-32=0$
• B. $x-4y+3=0$
• C. $2x+y-12=0$
• D. $y-2=0$

Answer 1

The correct option is C $2x+y-12=0$

$A(5,2)B(2,3)C(6,5)$
vertices of $D=(\frac{2+6}{2},\frac{5+3}{2})=(4,4)$
Let $A(5,2)D(4,4)$
Two point slope form,
$(x_1,y_1)(x_2,y_2)(5,2)(4,4)(y-2)=\frac{4-2}{4-5}(x-5)y-2=-2(x-5)2x-10=-y+22x+y-12=0$