Question

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

Answer 1

Answer:

X=3, Y=5

Step-by-step explanation:

Given ║gm ABCD with vertices A(1,2), B(4,3) & C(6,6)

let the point D be (x,y).Join AC & BD

In a parallelogram, diagonals bisect each other.

∴ mid-point of AC =mid-point of BD.....................eq.1

By midpoint formula,

mid-point of AC= 1+6/2 , 2+6/2

                          =7/2 , 8/2

                          =7/2 , 4

by eq.1; again by midpoint formula,

mid-point of BD=4+x/2=7\2 , 3+y/2=4

by cross-multiplying; 4+x=7[2 get cancelled] , 3+y=8

                                  =x=7-4 , y=8-3

                                  =x=3, y=5  

∴   vertices of D are (3,5)