Question

If (−1, 2), (2, −1) and (3, 1) are any three vertices of a parallelogram, then

(a) a = 2, b = 0

(b) a= −2, b = 0

(c) a = −2, b = 6

(d) a = 6, b = 2

Answer 1

Let ABCD be a parallelogram in which the co-ordinates of the vertices are A (−1, 2);

B (2,−1) and C(3, 1). We have to find the co-ordinates of the forth vertex.

Let the forth vertex be

Since ABCD is a parallelogram, the diagonals bisect each other. Therefore the mid-point of the diagonals of the parallelogram will coincide.

Now to find the mid-point of two points and we use section formula as,

The mid-point of the diagonals of the parallelogram will coincide.

So,

Therefore,

Now equate the individual terms to get the unknown value. So,

Similarly,

So the forth vertex is