The points (3, -4) and (-6, 2) are the extremities of a diagonal of a parallelogram. If the third vertex is (-1, -3). Find the coordinates of the fourth vertex.

Let three vertices be A(3, -4), B(-1, -3) and C(-6, 2) and fourth vertex be D(x, y)

It is given that quadrilateral joining these four vertices is parallelogram.

∴□ABCD is parallelogram

We know that diagonals of parallelogram bisect each other, ie midpoint of the diagonals coincide.

Let E(x_m , y_m) be the midpoint of diagonals AC and BD.

By midpoint formula,

x = , y =

For diagonal AC,

x_m = , y_m =

∴ x_m = , y_m =

∴ E(x_m , y_m) ≡ (, -1)

For diagonal BD,

= , -1 =

∴ x = -3 + 1 , y = -2 + 3

∴ x = -2 and y = 1

Hence, our fourth vertex is D(-2, 1)