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Prove that the points (3,\ 0),\ (4,\ ...

Prove that the points `(3,\ 0),\ (4,\ 5),\ (-1,\ 4)` and `(-2,\ -1)` , taken in order, form a rhombus. Also, find its area.

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RD SHARMA-COORDINATE GEOMETRY-All Questions
  1. Name the quadrilateral formed, if any, by the following points, and...

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  2. Find the equation of the perpendicular bisector of the line segment...

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  3. Prove that the points (3,\ 0),\ (4,\ 5),\ (-1,\ 4) and (-2,\ -1) , ...

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  4. Find a point on y-axis which is equidistant from the points (5,\ -2...

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  5. Find a relation between x and y such that the point (x ,\ y) is ...

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  6. If a point A(0,\ 2) is equidistant from the points B(3,\ p) and C(p...

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  7. Show that the points A(7, 10), B(-2, 5) and C(3, -4) are the vertices ...

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  8. If the point P(x ,\ 3) is equidistant from the points A(7,\ -1) ...

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  9. If A(3,\ y) is equidistant from points P(8,\ -3) and Q(7,\ 6) , fin...

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  10. If the point A(0,\ 2) is equidistant from the points B(3,\ p) an...

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  11. If the point P(k-1,\ 2) is equidistant from the points A(3,\ k) ...

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  12. Find the coordinates of the points which divides the line segment j...

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  13. In what ratio does the y-axis divide the line segment joining the p...

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  14. Find the ratio in which the point (-3,\ p) divides the line segm...

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  15. Point P divides the line segment joining the points A(-1,\ 3) and B...

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  16. Point P divides the line segment joining the points A(2,1)and B(5,-8) ...

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  17. Prove that (4,\ -1),\ (6,\ 0),\ (7,\ 2) and (5,\ 1) are the vertice...

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  18. If the points A(6,\ 1),\ \ B(8,\ 2),\ \ C(9,\ 4) and D(p ,\ 3) are ...

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  19. Find the lengths of the medians of a A B C whose vertices are A...

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  20. Find the coordinates of the point which divides the line segment jo...

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