Question

If A(1,2), B(4,y), C(x,6) and D(3,5) are the vertices of a

parallelogram taken in order, find x and y.​

Answer 1

Given :-

The points A ( 1 , 2 ), B ( 4 , y ), C ( x , 6 ) and D ( 3 , 5 ) are the vertices of a parallelogram.

To Find :-

• Value of x
• Value of y

Solution :-

We know,

In a parallelogram diagonals bisects each other.

That is,

Midpoint of AC = Midpoint of BD

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

Midpoint of AC :-

$\longrightarrow \sf \left(\dfrac{1+x}{2} \ , \ \dfrac{6+2}{2} \right) \\\\\longrightarrow \left( \dfrac{1+x}{2} \ , \ \dfrac{8}{2} \right) \\\\\longrightarrow \left( \dfrac{1+x}{2} \ , \ 4 \right)$

Midpoint of BD :-

$\longrightarrow \sf \left(\dfrac{4+3}{2} \ , \ \dfrac{y+5}{2} \right) \\\\\longrightarrow \left( \dfrac{7}{2} \ , \ \dfrac{y+5}{2} \right)$

$\longrightarrow \sf \dfrac{1+x}{2} = \dfrac{7}{2} \\\\\longrightarrow 1+x = 7 \\\\\longrightarrow \bf x = 6$

$\longrightarrow \sf \dfrac{y+5}{2} = 4 \\\\\longrightarrow y+5 = 8 \\\\\longrightarrow \bf y = 3$