Question

A(-1,0),B(1,3) and D(3,5) are the vertices of a parrallelogram ABCD. Find the co-ordinates of C

Answer 1

here are given 3 vertecies of a parrallelogram are A(-1,2) ,B(1,3) D(3,5)
let the coordinates of D are (X,Y) 
mid point of BD = mid point of AC because diagonals bisect each other in parrallelogram 
here we find buddy => 
mid points of line segement joining the point (x1,y1)and (x2,y2)  => x=(x1+x2)/2 
and for y=>(y1+y2)/2
x1= (x-1)/2  and y1= (y+0)/2 = y/2  
(x1,y1) = (2,4) 
(x-1)/2 = 2   and for y which means  y/2 = 4 so y=8 
x= 5  
hence the coordinates of c are (5,8) 
 

Answer 2

A( -1, 0) , B ( 1,3) and D ( 3, 5) are the vertices of parallelogram.

we know , according to Parallelogram property ,

midpoint of both both diagonals are same .
e.g

mid point of AC = midpoint of BD

let point C = (x , y)

use section formula, for midpoint

midpont of AC = { (x-1)/2, (y)/2}
midpoint of BD = { (1 + 3)/2, (3 +5)/2}

x -co-ordinate of midpoint of AC = x-co-ordinate of midpoint of BD

(x -1)/2 = (1+3)/2

x = 5

similarly for y-co-ordinate
( 3+5)/2 = (y)/2
y = 8

hence, point C = (5, 8)