Question

Q= 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

Midpoint of AC = Midpoint of BD

=> ( 4-2/2 , b+1/2) = (a+1/2 , 0+2/2)

=> ( 1 , b+1/2) = (a+1/2 , 1)

=> a+1/2 = 1 and b+1/2 = 1

=> a + 1 = 2 and b + 1 = 2

=> a = 1 and b =1

Answer 2

Answer:

a = 1, b = 1, AB = √10, BC = √10

Step-by-step explanation:

As we know the diagonals of a parallelogram bisect each other, we can take their midpoints.

Midpoint of diagonal AC = Midpoint of diagonal BD.

Given A(-2,1),B(a,0),C(4,b),D(1,2).

By using the formula (x1 + x2)/2 and (y1 + y2)/2 we have

 (-2 + 4)/2, (1 + b)/2 = (a + 1)/2 , (0 + 2)/2

on simplifying we get (b+1)/2 = 1 and (a+1)/2 = 1

So a = 1 and b = 1

Using the distance formula the length of parallelogram can be obtained.

AB = √(x2 - x1)^2 + (y2 - y1)^2

    = √(1 -(- 2)^2 + (0 -1)^2

   = √9 -1

AB = √10

BC = √(4 - 1)^2 + (1 - 0)^2

BC = √10

It is a rhombus since the sides are equal.