Question

if (1,2) ,(4,y ) ,(x,6) and(3,5) are tye vrrtices of a parallelogram taken in order, find the x and y
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Answer 1

Concept Used :-

Midpoint Formula :-

Let us assume a line segment joining the points A and B, and let C be the midpoint of AB, then coordinates of midpoint C (x, y) is given by

$\red{\underline{ \large\boxed{\rm \: (x, y) = (\dfrac{x_1 + x_2}{2}, \dfrac{y_1 + y_2}{2})}}}$

$\large\underline\purple{\bold{Solution -}}$

Let us assume a parallelogram ABCD having vertices,

• A (1, 2)

• B (4, y)

• C (x, 6)

• D (3, 5)

Now,

We know that,

• In parallelogram, diagonals bisect each other.

$\pink{\rm :\implies\:midpoint \: of \: AC = midpoint \: of \: BD}$

So,

• Using midpoint Formula, we get

$\rm :\implies\:(\dfrac{1 + x}{2} , \dfrac{2 + 6}{2} ) \: = \: (\dfrac{4 + 3}{2} , \dfrac{y + 5}{2} )$

• On comparing, we get

$\rm :\implies\: \blue{1 + x = 7} \: \: and \: \green{y + 5 = 8}$

$\rm :\implies\: \boxed{ \blue{x \: = \: 6}} \: \: and \: \: \boxed{ \green{y \: = \: 3}}$