Question

3 vertices of a parallelogram taken in order are (1,2) (2,4) (3,7) find its 4th vertex

Answer 1

Answer:

A [1,2] B [2,4] C [3,7 ]    let D [x,y]

In a parallelogram  mid points of diagonal are same

so midpoint of AC =  midpoint of BD

[ [ (1+3) /2 , (2+7) /2] = [ (2 + x) /2 , (4 + y) /2 ]

[ 4 /2 , 9 /2] = [ (2 + x) /2 , (4 + y) /2 ]

[ 2 , 9/2] = [ (2 + x) /2 , (4 + y) /2 ]

(2 + x) /2 =2   and   (4 + y) /2 = 9/2

2 +x = 4       and    4 + y = 9

x =2      and  y =5

D [2 ,5]