If A(1,2) , B(4,3 ) and C( 6,6) are the three vertices of a parallelogram ABCD , find the coordinates - Maths - Coordinate Geometry

Question

If A(1,2) , B(4,3 ) and C( 6,6) are the three vertices of a
parallelogram ABCD , find the coordinates of the fourth vertex
D

Chetna Khanna · Accepted Answer

Let A(1, 2), B (4, 3) and C(6, 6) Let D (x, y) be the fourth vertex of the parallelogram ABCD $Mid point of AC = (\frac{1 + 6}{2}, \frac{2 + 6}{2}) = (\frac{7}{2}, 4) Also, mid point of BD = (\frac{x + 4}{2}, \frac{y + 3}{2})$ Since, the diagonals of parallelogram bisect each other at O âˆ´ Mid point of BD = Mid point of AC $(\frac{x + 4}{2}, \frac{y + 3}{2}) = (\frac{7}{2}, 4) \Rightarrow \frac{x + 4}{2} = \frac{7}{2}, \frac{y + 3}{2} = 4 \Rightarrow x = 3, y = 3$ Thus, (3, 3) is the fourth vertex

If A(1,2) , B(4,3 ) and C( 6,6) are the three vertices of a parallelogram ABCD , find the coordinates of the fourth vertex D