If the points A(a

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

To find:  the values of a and b.

Solution:


Given points are A(a, -11), B(5, b), C(2, 15) and D(1, 1) and let the intersection of diagonals be E(x_m , y_m )

It is given that □ABCD is a parallelogram.

By midpoint formula.

x = , y =

We know that midpoint of parallelogram coincide.

∴ Midpoint of AC = Midpoint of BD

∴ ( , ) = ( , )

∴ = and =












⇒ a + 2 = 6 and 4 = b + 1

⇒ a = 6 - 2 and 4 - 1 = b

⇒ a = 4 and 3 = b

∴a = 4 and b = 3