Question

If the points (1,2) ; (2,a); (b,3) and (4,6) taken in order form a parallelogram. Find the values of a and b...

Answer 1

Let the points be A(1,2),(2,a),(b,3) and (4,6).

We know that Diagonals of a parallelogram bisect each other.

Midpoint of AC:

$( \frac{1 + b}{2}, \frac{2 + 3}{2} )$

$( \frac{1 + b}{2} , \frac{5}{2})$



Midpoint of BD:

$( \frac{2 + 4}{2}, \frac{a + 6}{2})$

$( \frac{6}{2}, \frac{a+6}{2} )$

$(3, \frac{a+6}{2})$


Midpoint of AC = Midpoint of BD

$( \frac{1 + b}{2}, \frac{5}{2}) = ( 3, \frac{a+6}{2})$

$\frac{1 + b}{2} = 3$  and $\frac{a+6}{2} = \frac{5}{2}$

1 + b = 6  and a + 6 = 5

b = 6 - 1 and a = 5 - 6

b = 5 and a = -1.


Hope this helps!