Home
Class 11
MATHS
In a triangle A B C ,A=(alpha,beta)B=(2,...

In a triangle `A B C ,A=(alpha,beta)B=(2,3),a n dC=(1,3)dot` Point `A` lies on line `y=2x+3,` where `alpha in Idot` The area of ` A B C ,` , is such that `[Delta]=5` . The possible coordinates of `A` are (where [.] represents greatest integer function). (a)`(2,3)` (b) `(5,13)` `(-5,-7)` (d) `(-3,-5)`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • SEQUENCES AND SERIES

    CENGAGE ENGLISH|Exercise All Questions|508 Videos

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE ENGLISH|Exercise All Questions|983 Videos

Similar Questions

Explore conceptually related problems

In a A B C ,A-=(alpha,beta),B-=(1,2),C-=(2,3), point A lies on the line y=2x+3, where alpha,beta are integers, and the area of the triangle is S such that [S]=2 where [ . ] denotes the greatest integer function. Then the possible coordinates of A can be (a) (-7,-11) (b) (-6,-9) (c) (2,7) (d) (3,9)

In a A B C ,A-=(alpha,beta),B-=(1,2),C-=(2,3), point A lies on the line y=2x+3, where alpha,beta are integers, and the area of the triangle is S such that [S]=2 where [ . ] denotes the greatest integer function. Then the possible coordinates of A can be (-7,-11) (-6,-9) (2,7) (3,9)

If [f((sqrt(3))/2)] is [.] denotes the greatest integer function) 4 (b) 5 (c) 6 (d) -7

The area of triangle A B C is 20c m^2dot The coordinates of vertex A are -5,0) and those of B are (3,0)dot The vertex C lies on the line x-y=2 . The coordinates of C are (a) (5,3) (b) (-3,-5) (-5,-7) (d) (7,5)

Find the value of x in [1,3] where the function [x^2+1]([dot] represents the greatest integer function) is discontinuous.

If A , B , C are three real numbers and p=[A+B+C] and q=[A]+[B]+[C]dot (where [.] represents greatest integer function). Then maximum value of [p-q] is: 1 (b) 0 (c) 2 (d) 3

If [x]^2-5[x]+6=0, where [.] denotes the greatest integer function, then x in [3,4] (b) x in (2,3] (c) x in [2,3] (d) x in [2,4)

If alphaa n dbeta are roots of the quadratic equation a x^2+b x+c=0 and a+b+c >0,a-b+c >0&c<0,t h e n[alpha]+[beta] is equal to (where [dot] denotes the greatest integer function) (a) 10 (b) -3 (c) -1 (d) 0

If the centroid of triangles formed by the vertices (1, 2, 3), (2, 1, 0) and (3, 1, 4) is (alpha, beta, gamma) then the value of [alpha]+[beta]+[gamma], where [ ] represents the greatest integer function, is _______.

Let A(−4,0) , B(4,0) & C(x,y) be points on the circle x^2 + y^2 = 16 such that the number of points for which the area of the triangle whose vertices are A, B and C is a positive integer, is N then the value of [N/7] is, where [⋅] represents greatest integer function.

CENGAGE ENGLISH-STRAIGHT LINES-All Questions
  1. Two sides of a triangle are along the coordinate axes and the medians ...

    Text Solution

    |

  2. The graph of y^2+2x y+40|x|=400 divides the plane into regions. Then ...

    Text Solution

    |

  3. In a triangle A B C ,A=(alpha,beta)B=(2,3),a n dC=(1,3)dot Point A l...

    Text Solution

    |

  4. If the straight lines 2x+3y-1=0,x+2y-1=0,and a x+b y-1=0 form a trian...

    Text Solution

    |

  5. Let O be the origin. If A(1,0)a n dB(0,1)a n dP(x , y) are points such...

    Text Solution

    |

  6. If the area of the rhombus enclosed by the lines l x+-m y+-n=0 is 2 s...

    Text Solution

    |

  7. In a triangle A B C , the bisectors of angles Ba n dC lies along the...

    Text Solution

    |

  8. If a/(b c)-2=sqrt(b/c)+sqrt(c/b), where a , b , c >0, then the family ...

    Text Solution

    |

  9. P(m , n) (where m , n are natural numbers) is any point in the interio...

    Text Solution

    |

  10. A diagonal of rhombus A B C D is member of both the families of lines ...

    Text Solution

    |

  11. A regular polygon has two of its consecutive diagonals as lines sqrt(3...

    Text Solution

    |

  12. Find the locus of the circumcenter of a triangle whose two sides are ...

    Text Solution

    |

  13. A line L1-=3y-2x-6=0 is rotated about its point of intersection with t...

    Text Solution

    |

  14. Straight lines y=m x+c1 and y=m x+c2 where m in R^+, meet the x-axis ...

    Text Solution

    |

  15. Show that the reflection of the line a x+b y+c=0 on the line x+y+1=0 i...

    Text Solution

    |

  16. Two equal sides of an isosceles triangle are 7x-y+3=0 and x+y-3=0. Its...

    Text Solution

    |

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

    Text Solution

    |

  18. In a triangle A B C , if A is (2,-1),a n d7x-10 y+1=0 and 3x-2y+5=0...

    Text Solution

    |

  19. The sides of a triangle are the straight line x+y=1, 7y=x, and sqrt(3)...

    Text Solution

    |

  20. One of the diameter of a circle circumscribing the rectangle ABCD is 4...

    Text Solution

    |