Question

A(-2.1), b(a,0), c(4.B) and d(1.2) are the vertices of a parallelogram abcd, find the team
b. Hence find the lengths of its sides. Or

Answer 1

Answer:

refer to the attachment.....

we know that the diagonals of a parallelogram bisect each other. show the midpoint of every diagonal will be the same. let this midpoint is O

therefore the midpoint of AC and BD is same

midpoint of AC is

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

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

midpoint of BD is

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

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

now .... therefore

(a+1)/2=1

=>a=1

and

(b+1)/2=1

=>b=1

the length of its sides are AB and BC

AB=√[(-2-1)²+(1-0)²]

=√10

BC=√[(1-4)²+(0-1)²]=√10

so the parallegram is a rhombus