Q3 of 23 Page 215

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)


More from this chapter

All 23 →
1

What are the coordinates of the fourth vertex of the parallelogram shown on the right?

 2

In this picture, the mid points of the sides of the large triangle are joined to make a small triangle inside.


Calculate the coordinates of the vertices of the large triangle.

 4

Prove that in any parallelogram, the sum of the square of all sides is equal to the sum of the squares of the diagonals.

 1

The coordinates of two points A, B are (3, 2) and (8, 7).

i) Calculate the coordinates of the point P on AB such that AP : PB = 2 : 3


ii) Calculate the coordinates of the point Q on AB such that AQ : QB = 3 : 2