Home
Class 12
MATHS
Let A,B,C be angles of triangles with ve...

Let A,B,C be angles of triangles with vertex `A -= (4,-1)` and internal angular bisectors of angles B and C be `x - 1 = 0` and `x - y - 1 = 0` respectively.
Slope of BC is

A

`1//2`

B

2

C

3

D

12

Text Solution

Verified by Experts

The correct Answer is:
B

Image of `A(4,-1)` in bisectors of B and C lies on side BC
`rArr` Image of `A(4,-1)` with respect to `x-y -1 =0` is
`(x-4)/(1) =(y+1)/(-1) =-(2(4+1-1))/(2) rArr (0,3)`
Image of `A(4,-1)` with respect to `x -1 =0` is
`(x-4)/(1) =(y+1)/(0) =- (2(4-1))/(1) rArr (-2,-1)`
Hence, slope of BC is `m = ((3+1)/(0+2)) =2`
Promotional Banner

Topper's Solved these Questions

  • STRAIGHT LINE

    CENGAGE PUBLICATION|Exercise Single Correct Answer Type|32 Videos

  • STRAIGHT LINE

    CENGAGE PUBLICATION|Exercise Multiple Correct Answers Type|8 Videos

  • STATISTICS

    CENGAGE PUBLICATION|Exercise Archives|10 Videos

  • STRAIGHT LINES

    CENGAGE PUBLICATION|Exercise ARCHIVES (NUMERICAL VALUE TYPE)|1 Videos

Similar Questions

Explore conceptually related problems

Let A,B,C be angles of triangles with vertex A -= (4,-1) and internal angular bisectors of angles B and C be x - 1 = 0 and x - y - 1 = 0 respectively. If A,B,C are angles of triangle at vertices A,B,C respectively then cot ((B)/(2))cot .((C)/(2)) =

In triangleABC , vertex A is (1, 2). If the internal angle bisector of angle B is 2x- y+10=0 and the perpendicular bisector of AC is y = x, then find the equation of BC

The vertex A of DeltaABC is (3,-1). The equation of median BE and angle bisector CF are x-4y+10=0 and 6x+10y-59=0, respectively. Equation of AC is

In a triangle ABC, coordinates of A are (1,2) and the equations of the medians through B and C are x+y=5 and x=4 respectively. Find the coordinates of B and C.

Let A B C be a triangle. Let A be the point (1,2),y=x be the perpendicular bisector of A B , and x-2y+1=0 be the angle bisector of /_C . If the equation of B C is given by a x+b y-5=0 , then the value of a+b is (a) 1 (b) 2 (c) 3 (d) 4

In A B C , the coordinates of the vertex A are (4,-1) , and lines x-y-1=0 and 2x-y=3 are the internal bisectors of angles Ba n dC .Then, the radius of the encircle of triangle A B C is (a) 4/(sqrt(5)) (b) 3/(sqrt(5)) (c) 6/(sqrt(5)) (d) 7/(sqrt(5))

In triangle A B C , the equation of the right bisectors of the sides A B and A C are x+y=0 and y-x=0 , respectively. If A-=(5,7) , then find the equation of side B Cdot

In a triangle A B C , the bisectors of angles Ba n dC lies along the lines x=y a n d y=0. If A is (1,2) , then the equation of line B C is

The angular points of a triangle are A(-1,-7),B(5,1)andC(1,4) . The equation of the bisector of the angle angleABC is