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 orthocenter of the triangle is

A

A. `(sqrt5,0)`

B

B. `(0,0)`

C

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

D

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 PUBLICATION|Exercise Multiple correct|13 Videos

  • COORDINATE SYSYEM

    CENGAGE PUBLICATION|Exercise Linked|10 Videos

  • COORDINATE SYSYEM

    CENGAGE PUBLICATION|Exercise Concept applications 1.6|9 Videos

  • COORDINATE SYSTEM

    CENGAGE PUBLICATION|Exercise Multiple Correct Answers Type|2 Videos

  • CROSS PRODUCTS

    CENGAGE PUBLICATION|Exercise DPP 2.2|13 Videos

Similar Questions

Explore conceptually related problems

If the ratio of three sides of a triangle be sqrt(2) : sqrt(3) : sqrt(5) , then the triangle is always a right-angled triangle.

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 orthocentre of a triangle whose vertices are (0,0),(sqrt3,0) and (0,sqrt6) is

If the angles of a triangle are 30^0a n d45^0 and the included side is (sqrt(3)+1)c m then the area of the triangle is______.

Find the incentre of the triangle with vertices (1, sqrt3), (0, 0) and (2, 0)

If the point (0,0),(2,2sqrt(3)), and (p,q) are the vertices of an equilateral triangle, then (p ,q) 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 A is

Find the area of the triangle vertices are (-5, -1), (3, -5), (5, 2)

A(0,sqrt(2))andB(2sqrt(2),0) are two vertices of a triangle ABC and AB=BC . If the equation of the side BC be x=2sqrt(2) , then the area of triangle ABC is (in sq . Units )-

If the angles of a triangle are 30^0a n d45^0 and the included side is (sqrt(3)+1) cm, then area of the triangle is 1/2(sqrt(3)+1)sq units area of the triangle is 1/2(sqrt(3)-1)sq units

CENGAGE PUBLICATION-COORDINATE SYSYEM -Exercises
  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)),(q r ,1/(q r)), and (r p...

    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 Delta ABC 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 in triangle ABC, A=(1, 10), circumcentre=(-1/3, 2/3) and orthocentr...

    Text Solution

    |

  8. In the DeltaABC, the coordinates of B are (0, 0), AB=2, /ABC=pi/3 and ...

    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.

    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 m...

    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

    |