Question

if (1, -2), (3, 6) , (x, 10) and (3, 2) are the vertices of a parallelogram taken in order, then the value of x is​

Answer 1

Solution :-

Let the points be :-

A ( 1 , -2 )

B ( 3 , 6 )

C ( x , 10 )

D ( 3 , 2 )

We know :-

In a parallelogram diagonals bisects each other.

That is,

Midpoint of AC = Midpoint BD

$\boxed{\bf Midpoint \ formula = \left( \dfrac{x_1+x_2}{2} \ , \ \dfrac{y_1+y_2}{2} \right)}$

Midpoint of AC :-

$\longrightarrow \sf \left( \dfrac{x+1}{2} \ , \ \dfrac{10-2}{2} \right) \\\\\longrightarrow \left( \dfrac{x+1}{2} \ , \dfrac{8}{2} \right) \\\\\longrightarrow \left( \dfrac{x+1}{2} \ , 4 \right)$

Midpoint of BD :-

$\longrightarrow \sf \left( \dfrac{3+3}{2} \ , \dfrac{2+6}{2} \right) \\\\\longrightarrow \left( \dfrac{6}{2} \ , \dfrac{8}{2} \right) \\\\\longrightarrow (3 \ , 4 )$

$\implies\sf \dfrac{x+1}{2}= 3 \\\\\implies x+1 = 6 \\\\\implies\bf x = 5$

Value of x = 5