Question

If (-2,-1) , (a,0) , (4,b) and (1,2) are the vertices of a parallelogram, find the values of a and b.

Answer 1

Hii friend,

Let A(-2,-1) , B(a,0) , C(4,b) and D(1,2) be the vertices of a parallelogram ABCD.

Join AC and BD, which intersect each other at O.

we know that,

The diagonals of a parallelogram bisect each other.

THEREFORE,

O is the midpoint of AC as well as BD.

Midpoint of AC = (X1+X2/2) , (Y1+Y2/2)

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

Midpoint of BD = (a+1/2 , 0+2/2) = (a+1/2 , 1)

THEREFORE,

a+1/2 = 1. and b-1/2 = 1

a+1 = 2. and b-1 = 2

a = 2-1. and b = 2+1

a = 1. and b = 3.

HENCE,

a = 1 and b = 3


HOPE IT WILL HELP YOU..... :-)

Answer 2

↑ Here is your answer ↓
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Diagonals of a parallelogram bisect each other {Theorem}

∴ AC = BC

$( \frac{-2+4}{2}, \frac{-1 + b}{2} ) = (\frac{a+1}{2}, \frac{0+2}{2})$

$( {1}, \frac{-1+b}{2}) = (\frac{a+1}{2}, 1)$  

$\frac{a+1}{2} = 1 | \frac{-1+b}{2} = 1$

$a + 1 = 2, -1 + b = 2$

Hence,

$a=1, b = 3$