# A parallelogram is drawn with the lines joining (x1, y1) and (x2, y2) to the origin as adjacent sides. What are the coordinates of the fourth vertex?

Let the coordinate of fourth vertex be (a1, b1) and the point of intersection of diagonals be (a2, b2)

Diagonals of a parallelogram bisects each other

According to the section formula for mid points

a2

a2 = 0.5(x1 + x2)

b2

b2 = 0.5(y1 + y2)

The point of intersection is (0.5(x1 + x2), 0.5(y1 + y2))

Again using the section formula for mid points

a1 = x1 + x2

b1 = y1 + y2

The fourth vertex of parallelogram is (x1 + x2, y1 + y2)

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