Question

If A (3,5), B(-5,-4),C(7,10) are vertices of the parallelogram taken in the order then find the coordinates of the fourth vertex

Answer 1

Co-ordinate of the fourth vertex is (15, 19).

EXPLAINATION

Theorem

Diagonals of a parallelogram bisect each other.

CALCULATION

Let (x, y) be the co-ordinate of the fourth vertex.

As mid point of the two diagonals are same, using section formula

$(\frac{3+7}{2},\frac{5+10}{2})=(\frac{-5+x}{2},\frac{-4+y}{2})$

$\frac{3+7}{2}=\frac{-5+x}{2},\frac{5+10}{2}=\frac{-4+y}{2}$

$10=-5+x, 15=-4+y$

$x=15, y= 19$

$(x, y) = (15, 19)$