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11th
Maths
Straight Lines
Introduction
If A( - 2, 1), B(a, 0), C(4...
MATHS
If A(−2,1),B(a,0),C(4,b) and D(1,2) are the vertices of a parallelogram ABCD, find the values of a and b. Hence find the lengths of its sides.
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ANSWER
Given sides of parallelogram A(−2,1),B(a,0),C(4,b),D(1,2)
We know that diagonals of Parallelogram bisect each other.
Mid-point let say O of diagonal AC is given by
x=(2x1+x2)and y=(2y1+y2)
O (2−2+4,21+b) ..................(1)
Mid-point let say P of diagonal BD is given by
P (2a+1,20+2) ..................(2)
Points O and P are same
Equating the corresponding co-ordinates of both midpoints, we get
2−2+4