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Prove that the points A(1, 1) , B(-1, -1...

Prove that the points `A(1, 1) , B(-1, -1) and C(sqrt(3), -sqrt(3))` are the vertices of an equilateral triangle.

A

right-angled

B

isoscles but not right angled

C

equilateral

D

name of these

Text Solution

Verified by Experts

The correct Answer is:
D
We have,
`AB=2sqrt(2),BCsqrt((3-1)^(2)+(sqrt(3)+1)^(2))=2sqrt(2)`
`and,AC=sqrt((3-1)^(2)+(sqrt(3)+1)^(2))=2sqrt(2)`
`:. AB=BC=CA`
So, `DeltaABC` is equilateral.
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OBJECTIVE RD SHARMA ENGLISH-CARTESIAN CO-ORDINATE SYSTEM -Exercise
  1. Prove that the points A(1, 1) , B(-1, -1) and C(sqrt(3), -sqrt(3)) are...

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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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