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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.

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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(xm , ym) be the midpoint of diagonals AC and BD. 

By midpoint formula,

∴ x = -3 + 1 , y = -2 + 3 

∴ x = -2 and y = 1 

Hence, 

our fourth vertex is D(-2, 1)

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