If the points (-2 , -1), (1, 0), (x, 3) and (1, y) form a parallelogram, find the values of x and y.

Let given points be A(-2, -1), B(1, 0), C(x, 3), D(1, y) 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 =

∴x = 4 and y = 2