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If the points `(x_(1),y_(1)), (x_(2),y_(2)), (x_(3),y_(3))and(x_(4),y_(4))` when joined successively produce a parallelogram, prove that `x_(1)+x_(3)=x_(2)+x_(4)andy_(1)+y_(3)=y_(2)+y_(4)`.

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CALCUTTA BOOK HOUSE-SECTION FORMULAS-EXERCISE-2
  1. If the points (x(1),y(1)), (x(2),y(2)), (x(3),y(3))and(x(4),y(4)) when...

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  2. The coordinates of the mid-point of the line segment obtained by joini...

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  3. The coordinates of the point which divides internally the line segment...

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  4. The coordinates of the point which divides externally the line segment...

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  5. The two end points of the diameter of a circle are (7, 9) and (-1, -3)...

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  6. The point of intersection of the medians of a triangle with vertices (...

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  7. (4, -3), (-5, 2) and (x, y) are the three vertices of a triangle. If t...

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  8. Determine the ratio into which the y-axis divides the line segment obt...

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  9. Find the ratio into which the line segment obtained by joining the poi...

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  10. (1, -2) and (-2, 3) are the points A and B of the DeltaABC. If the cen...

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  11. The coordinates of three consecutive vertices of a parallelogram are (...

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  12. The sides of the rectangle ABCD are parallel to the axes. If the coord...

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  13. P(1, 4), Q(3, -9) and R(-5, 2) are the vertices of a triangle. Find th...

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  14. Find the coordinates of the point at which the line segment obtained b...

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  15. Find the coordinates of the point at which the line segment obtained b...

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  16. Find the ratio into which the line segment obtained by joining the poi...

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  17. Find the ratio into which the line segment obtained by joining the poi...

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  18. Determine the ratio into which the line segment obtained by joining th...

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  19. If the points (3, 2), (6, 3), (x, y) and (6, 5) when joined successive...

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  20. (2, 1), (5, 4) and (1, 4) are three vertices of a parallelgram. Find t...

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  21. A(-3, 5) and B(1, 7) are two consecutive vertices of a parallelogram. ...

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