Question

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

(a)  2y = x + 7

(b)  7y =  x + 2

(c)  3y = x + 7

(d) 7y = x + 3

Answer 1

Correct option  (B)  7y = x + 3

Explanation :

 We have

Suppose the bisector of ABC meets the side AC at D (see Fig). Therefore, CD:DA = BC:BA = 5:10 = 1:2

Hence

Since B = (5, 1) and D = (1/3.1/3),  the equation of the bisector BD of ABC is

Hence, 7y = x + 3