Home
Class 12
MATHS
Let P = (-1, 0), Q = (0, 0) and R = (3, ...

Let P = (-1, 0), Q = (0, 0) and R = (3, `3sqrt3`) be three points. The equation of the bisector of the angle PQR

A

`(sqrt(3)//2)x+y= 0`

B

`x+sqrt(3)y= 0`

C

`sqrt(3)x+y= 0`

D

`x+(sqrt(3)//2)y= 0`

Text Solution

Verified by Experts

The correct Answer is:
C

The slope of QR is `(3sqrt(3)-0)//(3-0) = sqrt(3)`
`i.e., theta =60^(@)`
`"Clearly," anglePQR = 120^(@)`.
AQ is the angle bisector of the angle. So, line AQ makes `120^(@)` with the positive direction of the x-axis. Therefore, the equation of the bisector of `anglePQR` is
`y=x"tan" 120^(@) " or " y=-sqrt(3)x, i.e., sqrt(3)x+y=0`
Promotional Banner

Topper's Solved these Questions

  • STRAIGHT LINES

    CENGAGE PUBLICATION|Exercise EXERCISE (MULTIPLE CORRECT ANSWERS TYPE)|30 Videos

  • STRAIGHT LINES

    CENGAGE PUBLICATION|Exercise EXERCISE (LINKED COMPREHENSION TYPE)|27 Videos

  • STRAIGHT LINES

    CENGAGE PUBLICATION|Exercise CONCEPT APPLICATION EXERCISE 2.6|5 Videos

  • STRAIGHT LINE

    CENGAGE PUBLICATION|Exercise Multiple Correct Answers Type|8 Videos

  • THEORY OF EQUATIONS

    CENGAGE PUBLICATION|Exercise JEE ADVANCED (Numerical Value Type )|1 Videos

Similar Questions

Explore conceptually related problems

Let u=a x+b y+a ^3sqrt(b)=0,v=b x-a y+b^3sqrt(a)=0,a ,b in R , be two straight lines. The equations of the bisectors of the angle formed by k_1u-k_2v=0 and k_1u+k_2v=0 , for nonzero and real k_1 and k_2 are

If P(0,0,)Q(1,0)andR((1)/(2),(sqrt3)/(2)) are three given points, then the centre of the circle for which the lines PQ,QR and RP are the tangents is

The vertices of Delta PQR " are " P (2, 1) , Q (-2, 3) " and " R (4, 5) . Find equation of the median through the vertex R.

A point P moves on line 2x-3y+4=0 If Q(1,4) and R(3,-2) are fixed points, then the locus of the centroid of triangle PQR is a line: (a) with slope 3/2 (b) parallel to y-axis (c) with slope 2/3 (d) parallel to x-axis

If P-=(1,0), Q-=(-1, 0), R-=(2,0) are three given points, then the locus of the point S satisfying the condition SQ^2+SR^2=2SP^2 is

Let 2x-3y=0 be a given line and P(sintheta, 0) and Q(0, costheta) be the two points. Then P and Q lie on the same side of the given line, if theta lies in

P(3,1), Q(6,5) and R(x,y) are three points such that the angle PRQ is a right angle and the area of triangleRPQ=7 . Then the number of such points R is

Given that P(3,1),Q(6. 5), and R(x , y) are three points such that the angle P Q R is a right angle and the area of R Q P is 7, find the value of 4x-3y+5

Consider a triangle PQR with coordinates of its vertices as P(-8,5), Q(-15, -19), and R (1, -7). The bisector of the interior angle of P has the equation which can be written in the form ax+2y+c=0. The distance between the orthocenter and the circumcenter of triangle PQR is

Consider a triangle PQR with coordinates of its vertices as P(-8,5), Q(-15, -19), and R (1, -7). The bisector of the interior angle of P has the equation which can be written in the form ax+2y+c=0. triangle PQR is The sum a + c is

CENGAGE PUBLICATION-STRAIGHT LINES-EXERCISE (SINGLE CORRECT ANSWER TYPE)
  1. The equation of straight line which passes through the point (-4,3) su...

    Text Solution

    |

  2. A square of side 'a' lies above the x-axis and has one vertex at the o...

    Text Solution

    |

  3. Let P = (-1, 0), Q = (0, 0) and R = (3, 3sqrt3) be three points. The e...

    Text Solution

    |

  4. The equation of a line through the point (1, 2) whose distance from th...

    Text Solution

    |

  5. One diagonal of a square is along the line 8x-15 y=0 and one of its ve...

    Text Solution

    |

  6. Prove that the parallelogram formed by the lines x/a+y/b=1,x/b+y/a=1,x...

    Text Solution

    |

  7. A line with positive rational slope, passes through the point A(6,0) a...

    Text Solution

    |

  8. A projectile A is projected from ground. An observer B running on grou...

    Text Solution

    |

  9. Given A=(1,1) and A B is any line through it cutting the x-axis at Bdo...

    Text Solution

    |

  10. The number of possible straight lines passing through point(2,3) and f...

    Text Solution

    |

  11. Two parallel lines lying in the same quadrant make intercepts a and b ...

    Text Solution

    |

  12. The line L1-=4x+3y-12=0 intersects the x-and y-axies at Aa n dB , resp...

    Text Solution

    |

  13. A beam of light is sent along the line x-y=1 , which after refracting ...

    Text Solution

    |

  14. The number of integral values of m for which the x-coordinate of the p...

    Text Solution

    |

  15. If the sum of the distances of a point from two perpendicular lines in...

    Text Solution

    |

  16. The equation of set of lines which are at a constant distance 2 units...

    Text Solution

    |

  17. The lines y=m1x ,y=m2xa n dy=m3x make equal intercepts on the line x+y...

    Text Solution

    |

  18. Find the condition in a,b such that the portion of the line ax+by=1, i...

    Text Solution

    |

  19. The area of the triangle formed by the lines y= ax, x+y-a=0, and y-axi...

    Text Solution

    |

  20. The line x/a+y/b=1 meets the x-axis at A , the y-axis at B , and the l...

    Text Solution

    |