Question

Points A(3, 3), B(6, b) C(a,7) and D(5, 6) are vertices of a parallelogram ABCD. Find the
values of a and b.

Answer 1

Answer:

Let A(3, 3), B(6, y), C(x, 7) and D(5, 6) be the vertices of a parallelogram ABCD. Join Ac and BD, interesting each other at the point O.

We know that the diagonals of parallelogram bisect each other.

Therefore, O is the midpoint of AC as well as that of BD.

midpoint of AC is

and midpoint of BD is

But, these points coincide at the point O.

x + 3 = 11 and 6 + y =10

x = 8 and y = 4

Hence, x = 8 and y = 4.

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