Question

if(1,2),(4,y),(x,6) and (3,5) are the vertices of a parallelogram taken in order,find x and y.​

Answer 1

Answer:

Refer to the above attachments.

Hope it helps✌️

Answer 2

$\huge{\textbf{\textsf{\pink{Answer\::}}}}$

Let,

• A (1,2)

• B (4,y)

• C (x,6)

• D (3,5) are the vertices of a parallelogram ABCD.

• AC and BD are the diagonals .

• O is the midpoint of AC and BD.

Then, the coordinates of O are,

• $\sf\:{\bigg(\dfrac{1~+~x}{2}~,~\dfrac{2~+~6}{2}\bigg)}$

= $\bf\:{\bigg(\dfrac{1~+~x}{2}~,~4\bigg)}$

If, O is the mid-point of BD, then coordinates of O are,

• $\sf\:{\bigg(\dfrac{4~+~3}{2}~,~\dfrac{5~+~y}{2}\bigg)}$

= $\bf\:{\bigg(\dfrac{7}{2}~,~\dfrac{5~+~y}{2}\bigg)}$

Since, both coordinates are of the same point O.

$\sf\:{\therefore\:\dfrac{1~+~x}{2}~=~\dfrac{7}{2}~}$

$\sf\:{\implies\:1~+~x~=~7~}$

$\bf\orange\:{\implies\:x~=~6~}$

And,

$\sf\:{\therefore\:\dfrac{5~+~y}{2}~=~4~}$

$\sf\:{\implies\:5~+y~=~8~}$

$\bf\:{\implies\:y~=~3~}$

Hence,

• x = 6 & y = 3