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If (1,a), (2,b), (c^2,-3) are vertices o...

If `(1,a), (2,b), (c^2,-3)` are vertices of a triangle then the condition for its centroid to lie on x-axis is

A

a=3

B

b=3

C

`a+b=3`

D

`a-b=3`

Text Solution

Verified by Experts

The correct Answer is:
C
The coordinates of the centroid are `((3+c^(2))/(3),(a+b-3)/(3))`. It lies on a x-axis. So, its y-coordinates is zero
`:. (a+b-3)/(3)=0 rArr a+b=3`
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OBJECTIVE RD SHARMA ENGLISH-CARTESIAN CO-ORDINATE SYSTEM -Exercise
  1. If (1,a), (2,b), (c^2,-3) are vertices of a triangle then the conditio...

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  2. If the vertices of a triangle are at O(0, 0), A (a, 0) and B (0, a). T...

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  3. The angles A, B and C of a DeltaABC are in A.P. If AB = 6, BC =7,then...

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  4. If the distance between the points P (a cos 48^@, 0) and Q(0, a cos 12...

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  5. If the centroid of the triangle formed by the points (a ,\ b),\ (b ...

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  6. Write the coordinates of the orthocentre of the triangle formed by ...

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  7. If O is the origin P(2,3) and Q(4,5) are two, points, then OP*OQ cos ...

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  8. If O is the origin and P(x(1),y(1)), Q(x(2),y(2)) are two points then ...

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  9. If P(3,7) is a point on the line joining A(1,1) and B(6,16), then the ...

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  10. The coordinates of the centrid of a triangle having its circumcentre a...

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  11. The mid-point of the sides of a DeltaABC are D(6,1) ,E(3,5) and F(-1,-...

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  12. If the coordinates of orthocentre O' are centroid G of a DeltaABC are ...

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  13. The ratio in which the y-axis divides the line segement joining (4,6),...

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  14. If C and D are the points of internal and external division of line se...

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  15. If the centroid of a triangle is (1,\ 4) and two of its vertices...

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  16. A triangle with vertices (4, 0), (-1,-1), (3,5), is

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  17. The angle through which the coordinates axes be rotated so that xy-ter...

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  18. In order to make the first degree terms missing in the equation 2x^2+7...

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  19. When the origin is shifted to a suitable point, the equation 2x^2+y^2-...

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  20. If by shifting the origin at (1,1) the coordinates of a point P become...

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  21. By rotating the coordinates axes through 30^(@) in anticlockwise sens...

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