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Show that the points (-4, -7), (-1, 2), ...

Show that the points (-4, -7), (-1, 2), (8, 5) and (5, -4) taken in order are the vertices of a rhombus. Find its area.
(Hint : Area of rhombus `= (1)/(2)xx` product of its diagonals)

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The correct Answer is:
AB = BC = CD = DA = `sqrt(90)` , AC `ne` BD (vertices of a thombus), 72 Sq. units
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NCERT KANNAD-COORDINATE GEOMETRY -EXERCISE 7.1
  1. Find the distance between the following pairs of points : (2,3), (4,...

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  2. Find the distance between the following pairs of points : (-5, 7), (...

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  3. Find the distance between the pair of points (-2, -3) and (3, 2)

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  4. Find the distance between the following pairs of points : (a, b), (-...

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  5. Find the distance between the points (0, 0) and (36, 15).

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  6. Determine if the points (1, 5), (2, 3) and (-2, -11) are collinear.

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  7. Check whether (5, -2), (6, 4) and (7, 2) aare the vertices of as isoce...

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  8. Show that the following points form an equilateral triangle A(a, 0), B...

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  9. Prove that the points (-7, -3), (5, 10), (15, 8) and (3, -5) taken in ...

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  10. Show that the points (-4, -7), (-1, 2), (8, 5) and (5, -4) taken in or...

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  11. Name the type of quadrilateral formed, if any by the following points,...

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  12. Name the type of quadrilateral formed, if any by the following points,...

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  13. Name the type of quadrilateral formed, if any by the following points,...

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  14. Find the point on the x-axis which is equidistant from (2, -5) and (-2...

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  15. If the distance between two points (x, 7) and (1, 15) is 10, find the ...

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  16. Find the values of y for which the distance between the points P(2, -3...

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  17. Find the radius of the circle whose centre is (3, 2) and passes throug...

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  18. Can you draw a triangle with vertices (1, 5), (5, 8) and (13, 14) ? Gi...

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

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