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If the vertices of a triangle are `(sqrt(5,)0)` , (`sqrt(3),sqrt(2))` , and `(2,1)` , then the orthocentre of the triangle is (a) `(sqrt(5),0)` (b) `(0,0)` `(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).
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CENGAGE ENGLISH-COORDINATE SYSYEM -Exercises
  1. If two vertices of a triangle are (-2,3) and (5,-1) the orthocentre li...

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

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

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

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  5. In Delta ABC if the orthocentre is (1,2) and the circumcenter is (0,0)...

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

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

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

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

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

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  11. Point P(p ,0),Q(q ,0),R(0, p),S(0,q) from.

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

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

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

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

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

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

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

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

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

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