    Question

# If A (–2, –1), B (a, 0), C (4, b) and D (1, 2) are the vertices of a parallelogram, find the values of a and b.

A
a = 1 and b = 3
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B
a = 2 and b = 3
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C
a = 1 and b = 1
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D
a = 1 and b = 4
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Solution

## The correct option is D a = 1 and b = 3We know that the diagonals of a parallelogram bisect each other. Therefore, the coordinates of the mid-point of AC are same as the coordinates of the mid-point of BD. The coordinates of the mid-point of a line formed by joining two points (x1,y1) and (x2,y2) are (x1+x22,y1+y22) Midpoint of AC = (−2+42,−1+b2) Midpoint of BD = (a+12,0+22) ⇒ (−2+42,−1+b2) = (a+12,0+22) ⇒ (1,b−12)=(a+12,1) ⇒ a+12 = 1 and b−12 = 1 ⇒ a + 1 = 2 and b - 1 = 2 ⇒ a = 1 and b = 3  Suggest Corrections  0      Similar questions  Related Videos   Midpoint Formula
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