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

Solution :-

Let :-

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

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 :-

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

Midpoint of BD :-

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

$\longrightarrow \sf \dfrac{x+1}{2}= \dfrac{7}{2} \\\\\longrightarrow 2(x+1) = 14 \\\\\longrightarrow 2x+2 = 14 \\\\\longrightarrow 2x= 12 \\\\\longrightarrow \bf x = 6$

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

Value of x = 6

Value of y = 3

Answer 2

Answer:

Given :

• if (1,2) ,(4,y) ,(x,6) and (3,5) are the vertices of a parallelogram

To Find :

• find x and y

Solution :

• A parallelogram is a quadrilateral of which opposite sides are parallel and opposite angle are equal.

Let A(1,2) B(4,y) C(x,6) D(3,5) In a parallelogram ABCD

Coordinates of A = {sum of coordinates of B and D} - {coordinates of C}

Putting all Value :

1 = 4 + 3 - x

1 = 7 - x

x = 7 - 1

x = 6

The Values of x is 6

2 = y + 5 - 6

2 = y - 1

y = 2 + 1

y = 3

The Values of y is 3