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The vertices of a triangle are (a, 0), (...

The vertices of a triangle are (a, 0), (-a, 0) and `(0, sqrt(3a))`. Show that the triangle is equilateral.

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KALYANI PUBLICATION-Co-ordinate Geometry-EXERCISE
  1. Show that the triangle whose vertices are (1, 4), (-5, 1) and (1, -2) ...

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  2. Prove that the triangle whose vertices are (-2, 2) (1, -2) and (9, 4) ...

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  3. The vertices of a triangle are (a, 0), (-a, 0) and (0, sqrt(3a)). Show...

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  4. If the points (p, q) and (q, p) are equidistant from the point (x, y)....

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  5. Under what condition the points (3, - 4) and (-5, 2) are equidistant f...

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  6. Prove that the point (-2, -11) is equidistant from the points (-3, 7) ...

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  7. If the square of the distance between the points (5, 10) and (10, y) b...

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  8. One extremity of a straight line 10 cm long is (-3, 2). If the ordinat...

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  9. If the extremities of a circle be (-5, 7) and (3, -11), find the centr...

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  10. Find the coordinate of a point equidistant from the given points A(2, ...

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  11. Find the co-ordinate of a point equidistant from the given point A(1, ...

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  12. Prove that the points (-1, 0), (3, 1), (2, 2), (-2, 1) are the vertice...

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  13. Prove that the points (- 1, 0), (0, 3), (1, 3) and (0, 0) are the vert...

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  14. Prove that the points (-2, –1), (1, 0), (4, 3), (1,2) are not the ver...

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  15. Prove that the points (a, b), (a, -b), (-a, b) and (-a, -b) are the ve...

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  16. Show that the quadrilateral with the vertices (3, 2), (0, 5), (-3, 2),...

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  17. Show that the quadrilateral with the vertices (0, 0), (a, 0), (a, a), ...

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  18. Show that the quadrilateral with the vertices (7, 3), (3, 0), (0, -4),...

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  19. Prove that (3, 4), (4, 2), (5, 4) and (4, 6) are the vertices of a rho...

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  20. If the co-ordinates of the points P, Q, S are (at^2, 2at), (a/t^2, (2...

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