Home
Class 12
MATHS
If the vertices of a triangle are (sqrt(...

If the vertices of a triangle are `(sqrt(5,)0)` , (`sqrt(3),sqrt(2))` , and `(2,1)` , then the orthocentre of the triangle is `(sqrt(5),0)` (b) `(0,0)` (c)`(sqrt(5)+sqrt(3)+2,sqrt(2)+1)` (d) none of these

A

`(sqrt5,0)`

B

`(0,0)`

C

`(sqrt5+sqrt3+2,sqrt2+1)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
The circumcenter of the triangle is (0,0) as vertices are at equal distance from (0,0). So, the orthocenter will be (sum of x-coordinates, sum of y-coordinates).
Promotional Banner

Topper's Solved these Questions

  • COORDINATE SYSYEM

    CENGAGE|Exercise Exercise (Multiple)|13 Videos

  • COORDINATE SYSYEM

    CENGAGE|Exercise Exercise (Comprehension)|10 Videos

  • COORDINATE SYSYEM

    CENGAGE|Exercise Exercise 1.6|9 Videos

  • COORDINATE SYSTEM

    CENGAGE|Exercise Multiple Correct Answers Type|2 Videos

  • CROSS PRODUCTS

    CENGAGE|Exercise DPP 2.2|13 Videos

Similar Questions

Explore conceptually related problems

The incentre of the triangle with vertices (1, sqrt3 ) (0,0) (2,0) is

P is a point on the line y+2x=1, and Q and R two points on the line 3y+6x=6 such that triangle P Q R is an equilateral triangle. The length of the side of the triangle is (a) 2/(sqrt(5)) (b) 3/(sqrt(5)) (c) 4/(sqrt(5)) (d) none of these

The incentre of a triangle with vertices (7, 1),(-1, 5) and (3+2sqrt(3),3+4sqrt(3)) is

The vertices of a triangle are (0,0), (x ,cosx), and (sin^3x ,0),w h e r e0ltxltpi/2 the maximum area for such a triangle in sq. units is (a) (3sqrt(3))/(32) (b) (sqrt(3)/32) (c) 4/32 (d) (6sqrt(3)) /(32)

The value of alpha such that sin^(-1)2/(sqrt(5)),sin^(-1)3/(sqrt(10)),sin^(-1)alpha are the angles of a triangle is (-1)/(sqrt(2)) (b) 1/2 (c) 1/(sqrt(3)) (d) 1/(sqrt(2))

Prove that (sqrt(2),sqrt(2)) (-sqrt(2), -sqrt(2) ) and (-sqrt(6 ) , sqrt(6)) are ther vertices of an equilateral triangle.

Let the area of triangle ABC be (sqrt3 -1)//2, b = 2 and c = (sqrt3 -1), and angleA be acute. The measure of the angle C is

Let the area of triangle ABC be (sqrt3 -1)//2, b = 2 and c = (sqrt3 -1), and angleA be acute. The measure of the angle C is

Prove that the points (0,0) (3, sqrt(3)) and (3, -sqrt(3)) are the vertices of an equilateral triangle.

The sum up to n terms of the series 1/(sqrt(1) + sqrt(3)) + 1/(sqrt(3) + sqrt(5)) + 1/(sqrt(5) + sqrt(7)) +… is:

CENGAGE-COORDINATE SYSYEM -Exercise (Single)
  1. If two vertices of a triangle are (-2,3) and (5,-1) the orthocentre li...

    Text Solution

    |

  2. The vertices of a triangle are (p q ,1/(p q)),(p q)),(q r ,1/(q r)), a...

    Text Solution

    |

  3. If the vertices of a triangle are (sqrt(5,)0) , (sqrt(3),sqrt(2)) , an...

    Text Solution

    |

  4. Two vertices of a triangle are (4,-3) & (-2, 5). If the orthocentre o...

    Text Solution

    |

  5. In A B C , if the orthocentre is (1,2) and the circumcenter is (0, 0)...

    Text Solution

    |

  6. A triangle A B C with vertices A(-1,0),B(-2,3/4), and C(-3,-7/6) has i...

    Text Solution

    |

  7. If a triangle A B C ,A-=(1,10), circumcenter -=(-1/3,2/3), and orthoce...

    Text Solution

    |

  8. In A B C , the coordinates of B are (0,0),A B=2,/A B C=pi/3, and the ...

    Text Solution

    |

  9. If the origin is shifted to the point ((a b)/(a-b),0) without rotation...

    Text Solution

    |

  10. A light ray emerging from the point source placed at P(2,3) is reflect...

    Text Solution

    |

  11. Point P(p ,0),Q(q ,0),R(0, p),S(0,q) from (a)parallelogram (b)rhombus ...

    Text Solution

    |

  12. A rectangular billiard table has vertices at P(0,0),Q(0,7),R(10 ,7), a...

    Text Solution

    |

  13. ABCD is a square Points E(4,3) and F(2,5) lie on AB and CD, respective...

    Text Solution

    |

  14. If one side of a rhombus has endpoints (4, 5) and (1, 1), then the ...

    Text Solution

    |

  15. A rectangle A B C D , where A-=(0,0),B-=(4,0),C-=(4,2)D-=(0,2) , under...

    Text Solution

    |

  16. If a straight line through the origin bisects the line passing through...

    Text Solution

    |

  17. Let Ar ,r=1,2,3, , be the points on the number line such that O A1,O ...

    Text Solution

    |

  18. The vertices of a parallelogram A B C D are A(3,1),B(13 ,6),C(13 ,21),...

    Text Solution

    |

  19. Point A and B are in the first quadrant; point O is the origin. If the...

    Text Solution

    |

  20. Let a,b,c be in A.P and x,y,z be in G.P.. Then the points (a,x),(b,y) ...

    Text Solution

    |