Question

Three vertices of triangle ABC are A(-1, 11 ) B(- 9 - 8) C (15 - 2 ) the equation of angle bisector of angle A is

Answer 1

The equation of the angle bisector of ∠A is 4x + y = 7.

Step-by-step explanation:

We know that, the ratio in which the angle bisector divides the opposite side, divides the other two sides in the same ratio.

Let D be the point on the side BC where the bisector of ∠A meets.

Thus BD : DC = BA : AC

Here BA = √{(- 1 + 9)² + (11 + 8)²} = √425 units

and AC = √{(15 + 1)² + (- 2 - 11)²} = √425 units

∴ BD : DC = 1 : 1

Let the coordinates of D are (p, q)

∴ p = (- 9 + 15)/(1 + 1) = 3, q = (- 8 - 2)/(1 + 1) = - 5

∴ the coordinates of D are (3, - 5)

∴ the equation of AD is

(y - 11)/(11 + 5) = (x + 1)/(- 1 - 3)

or, (y - 11)/16 = (x + 1)/(- 4)

or, y - 11 = - 4 (x + 1)

or, y - 11 = - 4x - 4

or, 4x + y = 7,

which is the required angle bisector.