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:

nice question friend. keep it. up

Answer 2

Step-by-step explanation:

AnswEr:

Let us Consider that A, B, C & D be the Points of the Parallelogram.

A(1,2), B(4,y), C(x,6) & D(3,5)

We know that, the diagonals of Parallelogram bisect each other.

Finding the value of x & y :-

$\dag\:\:\small\bold{\underline{\sf{\red{By\: Using\:Mid \:-\: Point\: Formula}}}}$

$:\implies\small{\underline{\boxed{\sf{\pink{\dfrac{x_1 \:+\; x_2}{2} \:,\: \dfrac{y_2\:+\;y_2}{2}}}}}}$

Diagonal AC

Here,

x1 = 1

x2 = x

y1 = 2

y2 = 6

★ Putting Values:-

$:\implies\sf\: \dfrac{1 \:+\:x}{2}\:,\:\dfrac{2\:+\:6}{2}$

$:\implies\sf \:\dfrac{1\:+\:x}{2}\:,\:4$

Now, Diagonal BC

Here,

x1 = 4

x2 = 3

y1 = 5

y2 = y

$:\implies\sf\:\dfrac{4 \:+\:3}{2}\:,\:\dfrac{5\:+\:y}{2}$

$:\implies\sf\: \dfrac{7}{2}\: , \: \dfrac{5\:+\:y}{2}$

Now, Mid points of Both Diagonals

$:\implies\sf\:\dfrac{1\:+\:X}{2} \:=\: \dfrac{7}{2} \: and \; 4 = \dfrac{5 \:+\: y}{2}$

$:\implies\sf\: x + 1 = 7$

$:\implies\sf\: x = 7 - 1$

$:\implies\large{\underline{\boxed{\sf{\blue{x\:=\:6}}}}}$

$\rule{150}2$

$:\implies\sf\: 5 + y = 8$

$:\implies\sf\: y = 8 - 5$

$:\implies\large{\underline{\boxed{\sf{\blue{y\:=\:3}}}}}$

$\bold{\underline{\sf{\pink{Hence,\: Value\: of \: x \: and \: y \: is \: 6 \: and \: 3.}}}}$