Question

If (2, 2), (1,0), (x, 0), (5, y) form a
parallelogram then (x, y) =​

Answer 1

Step-by-step explanation:

hope it's helpful for you

Answer 2

$Given \: (2,2), (1,0), (x,0) \:and \: (5,y) \: are$

$vertices \:of \: a \: parallelogram .$

$Let \: A(2,2) = ( x_{1} , y_{1})$

$B(1,0) = ( x_{2} , y_{2})$

$C(x,0) = ( x_{3} , y_{3})$

$and\: D(5,y) = ( x_{4} , y_{4})$

/* We know that ,

Diagonals bisects each other in a parallelogram */

$\pink {Mid \: point \:of \: AC = Mid \: point \:of \: BD}$

$\implies \Big( \frac{x_{1} + x_{3}}{2} , \frac{y_{1} + y_{3}}{2}\Big) = \Big( \frac{x_{2} + x_{4}}{2} , \frac{y_{2} + y_{4}}{2}\Big)$

$\implies \Big( \frac{2+x}{2} , \frac{2+0}{2}\Big) = \Big( \frac{ 1+5}{2} , \frac{0+y}{2} \Big)$

$\implies \Big( \frac{2+x}{2} , 1\Big) = \Big( 3 , \frac{y}{2} \Big)$

$\implies \frac{2+x}{2} = 3 \:and \: \frac{y}{2}= 1$

$\implies 2+ x = 6 \: and \: y = 2$

$\implies x = 4\: and \: y = 2$

Therefore.,

$\red{ ( x , y ) } \green { = ( 4, 2 ) }$

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