If the points A (a, -11), B (5, b), C (2, 15) and D (1, 1) are the vertices parallelogram ABCD, find the values of a and b.

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Solution

Since, the diagonals of a parallelogram bisect each other.

∴ Coordinates of the mid-point of AC = Coordinates of the mid-point of BD

so applying the mid point formula for diagonal AC

$x equals fraction numerator a plus 2 over denominator 2 end fraction y equals fraction numerator negative 11 plus 15 over denominator 2 end fraction y equals 4 over 2 equals 2$

now considering the diagonal BD

$x equals fraction numerator 1 plus 5 over denominator 2 end fraction equals 6 over 2 equals 3 y equals fraction numerator b plus 1 over denominator 2 end fraction equals 2 left parenthesis f r o m space t h e space r e s u l t space o f space d i a g o n a l space A C right parenthesis b plus 1 equals 4 b equals 3$
$sin c e space x equals 3 equals fraction numerator a plus 2 over denominator 2 end fraction 6 equals a plus 2 a equals 6 minus 2 a equals 4$

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A (- 2, 1), B (a, 0), C (4, b)

D (1, 2)

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