If two vertices of a parallelogram are (3, 2), (-1, 0) and its diagonals meet at (2, -5), find the other two vertices of the parallelogram.

The mid-point of the line segment joining the points (3, 2) and (-1, 0) is = (1, 1) which is not the same as (2, -5), therefore, the given points cannot be the opposite vertices. Hence, these vertices are adjoining. The below figure shows the parallelogram: Let coordinates of C be (x, y) then by mid-point formula, ⇒ x + 3 = 4 and y + 2 = -10 ⇒ x = 1 and y = -12. ∴ Coordinates of C are (1, -12). Now finding coordinates of D, let D be (m, n). Applying mid-point formula we get, ⇒ m - 1 = 4 and n = -10 ⇒ m = 5 and n = -10. ∴ Coordinates of D are (5, -10). Hence, the coordinates of C are (1, -12) and D are (5, -10).

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Mathematics

If two vertices of a parallelogram are (3, 2), (-1, 0) and its diagonals meet at (2, -5), find the other two vertices of the parallelogram.

Section Formula

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Three consecutive vertices of a parallelogram ABCD are A(1, 2), B(1, 0) and C(4, 0). Find the fourth vertex D.

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