dear sir...please help me with this ques.!

as we know that angle bisector bisects the oppiste side also which means the bisector of angle A will bisect side BC. So we need to find equation of the line which passes through A(-2,4) and mid point of BC.

mid point of BC = (5+4)/2 , (5-2)/2

= 9/2, 3/2

slope of the equation of the bisector is = (4-3/2)/(-2-9/2)

=(5/2)/(-13/2)

=-5/13

Equation of the line is :

y = mx + c

4 = (-5/13)(-2) + c

4 = 10/13 + c

4-10/13 = c

c = 42/13

y = (-5/13)x + 42/13

13y = -5x+42

13y+5x = 42