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in Coordinate Geometry by (49.2k points)
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If A (–2, –1), B (a, 0), C (4, b) and D (1, 2) are the vertices of a parallelogram the values of a and b respectively are 

(a) 3, 1 

(b) –3, 1 

(c) 1, 3 

(d) –1, –3

1 Answer

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Best answer

(c) 1, 3

The diagonals of a parallelogram bisect each other, therefore co-ordinates of mid-points of both the diagonals are the same co-ordinates of mid-point of diagonal AC

\(\bigg(\frac{4-2}{2},\frac{b-1}{2}\bigg) \) = \(\bigg(1,\frac{b-1}{2}\bigg) \)

Co-ordinate of mid-point of diagonal BD

\(\bigg(\frac{1+a}{2},\frac{2-0}{2}\bigg) \) = \(\bigg(\frac{1+a}{2},1\bigg) \)

⇒ \(\frac{1+a}{2}=1\) and \(\frac{b-1}{2}=1\)

⇒ 1 + a = 2 and b – 1 = 2 

a = +1 and b = 3

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