The vertices of a triangle are $A (- 1, - 7), B (5, 1),$ and $C (1, 4) .$ The equation of the bisector of $∠ A B C$ is ___

x-7y+2=0

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

7x+y-2=0

No worries! We‘ve got your back. Try BYJU‘S free classes today!

2y-7x-5=0

No worries! We‘ve got your back. Try BYJU‘S free classes today!

2x+7y+5=0

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A x-7y+2=0
Let BD be the bisector of $∠ A B C$ then,

$A D : D C = A B : B C a n d A B = \sqrt{(5 + 1)^{2} + (1 + 7)^{2}} = 10 B C = \sqrt{(5 - 1)^{2} + (1 - 4)^{2}} = 5 ∴ A D : D C = 2 : 1$
Therefore, by section formula, $D = (\frac{1}{3}, \frac{1}{3})$ therefore the equation of BD is
$y - 1 = \frac{\frac{1}{3} - 1}{\frac{1}{3} - 5} (x - 5) o r y - 1 = \frac{- \frac{2}{3}}{- \frac{14}{3}} (x - 5) o r 7 y - 7 = x - 5 x - 7 y + 2 = 0$

Suggest Corrections

Similar questions

Q. The angular points of a triangle are

A (- 1, - 7), B (5, 1)

and

C (1, 4)

. The equation of the bisector of the angle

∠ A B C

Q. P(3, 4), Q(7, -2) and R(-2, -1) are the vertices of a triangle PQR. Find the equation of the median of the triangle through R.

Q. The equation of the obtuse angle bisector of lines

12 x - 5 y + 7 = 0

and

3 y - 4 x - 1 = 0

Q. The vertices of a triangle are

A (- 1, - 7)

B (5, 1)

and

C (1, 4)

. The equation of the bisector of

∠

ABC is?

Find the equation of family of circles through the intersection of $x^{2} + y^{2} - 6 x + 2 y + 4 = 0$ and $x^{2} + y^{2} + 2 x - 4 y - 6 = 0$ whose center lies on $y = x .$

Join BYJU'S Learning Program

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

The correct option is A x-7y+2=0Let BD be the bisector of ∠ABC then, AD:DC=AB:BCand AB=√(5+1)2+(1+7)2=10BC=√(5−1)2+(1−4)2=5∴AD:DC=2:1 Therefore, by section formula, D=(13,13) therefore the equation of BD is y−1=13−113−5(x−5)or y−1=−23−143(x−5)or 7y−7=x−5x−7y+2=0

The vertices of a triangle are $A (- 1, - 7), B (5, 1),$ and $C (1, 4) .$ The equation of the bisector of $∠ A B C$ is ___