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

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 = 4 and b = 3