If A(-2,1),B(a,0),C(4,b), and D(4,5) are the vertices of a parallelogram,find the values of a and b.Hence find the length of its sides
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Let AC and BD intersect at O
((-2+4)/2 , (1+ b)/2) = ( (a + 4)/2 , (0 +5)/2)
(1, (1+ b)/2) = ( (a + 4)/2 , 5/2)
Comparing x and y coordinated
x:
1 = (a+4)/2
a = -2
y:
(1+ b)/2 = 5/2
b = 4
Now coordinates are:
A(-2,1),B(-2,0),C(4,4), and D(4,5)
AB = 1
BC = 2root13
CD = 1
AD= 2root13
((-2+4)/2 , (1+ b)/2) = ( (a + 4)/2 , (0 +5)/2)
(1, (1+ b)/2) = ( (a + 4)/2 , 5/2)
Comparing x and y coordinated
x:
1 = (a+4)/2
a = -2
y:
(1+ b)/2 = 5/2
b = 4
Now coordinates are:
A(-2,1),B(-2,0),C(4,4), and D(4,5)
AB = 1
BC = 2root13
CD = 1
AD= 2root13
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