if A (-2,1) B (a,0) C (4,b) and D (1,2) are the vertices of parallelogram ABCD, find the value of a and B. hence find the length of its side
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Answered by
7
find AB BC CD DA by applying distance formula opposite sides are parallel and equal in parallelogram
so put AB = CD
BC = DA
you will get two equation in form of a & b
after solving them
you will easily get a & b values
so put AB = CD
BC = DA
you will get two equation in form of a & b
after solving them
you will easily get a & b values
Answered by
26
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
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
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