Question

If A(-2, 1) and B(a, 0), C(4, b) and D( 1, 2) are the vertices of a parallelogram ABCD, find the values of a and b. Hence find the lengths of its sides​

Answer 1

Answer:

Step-by-step explanation:

In a parallelogram the diagonals bisect each other

Midpoint of AC = midpoint of BD

Midpoint formulae (x1+x2)/2 ; (y1+y2)/2

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

2/2 ; (1+b)/2 = (a+1)/2 ; 2/2

=> 1=(a+1)/2

a+1 = 2

a=1

=> (1+b)/2 = 1

1+b=2

b= 1

a=1 and b=1

Using distance formula we came find out the length of the sides of parallelogram

Distance formula √[(x2-x1)²+(y2-y1)²]

AB = √[(1+2)²+(0-1)²]

= √(9+1)

=√10u

BC = √[(4-1)²+(1-0)²]

= √(3²+1²)

= √10u

It is a rhombus as all the sides are equal