Let ABCD be a parallelogram such that the coordinates of its three vertices A, B, C are (1, 1), (3, 4) and (−2, 8), respectively. Then, the coordinates of the vertex D are
Explanation:
Let (x, y) be the coordinates of 4th vertex. In a parallelogram, diagonals bisect each other. ∴ Intersection point of diagonals is same as the mid-point of two opposite vertices.
Sum of coordinates of two pair of opposite vertices is same.
A and C are opposite vertices while B and D are opposite vertices.
(1, 1) is opposite (-2, 8) while (3, 4) is opposite (x, y) ⇒ 1 - 2 = 3 + x ⇒ x = -4 ⇒ 1 + 8 = 4 + y ⇒ y = 5 ∴ (x, y) = (-4, 5)
Of the three possibilities only (-4, 5) is mentioned in options.
Hence, option (c).
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