Question

if A(-2,1),B(a,0),C(4,b),D(1,2) are the vertices of a parallelogram ABC, find the values of a and b. Hence find the length of its sides

Answer 1

Given three of vertices of a parallelogram are A(1,2), B (4,3), C (6,6).
Let the coordinates of fourth vertex be D (x, y)
In a parallelogram, diagonals bisect each other.
Hence midpoint of BD = midpoint of AC
Midpoint of line segment joining the points  and  is 


4 + x = 7 and 
 and 3 + y = 8
 and y = 5
Therefore, the fourth vertex, D is (3, 5).
Given three of vertices of a parallelogram are A(1,2), B (4,3), C (6,6).
Let the coordinates of fourth vertex be D (x, y)
In a parallelogram, diagonals bisect each other.
Hence midpoint of BD = midpoint of AC
Midpoint of line segment joining the points  and  is 


4 + x = 7 and 
 and 3 + y = 8
 and y = 5
Therefore, the fourth vertex, D is (3, 5).

Answer 2

by using mid point formula we can find valu of a and b answer a=1 and b =1