Question

If (1, −2), (3, 6), (5, y) (x, 2) are the vertices of parallelogram, find the

value of x and y?​

Answer 1

$\huge \tt \colorbox{red}{given}$

==》(1, −2), (3, 6), (5,y ) (x, 2) are the vertices of parallelogram.

$\huge \bf \colorbox{green}{: to \: find}$

==》value of x and y?

$\huge \fcolorbox{red}{gr}{solution}$

==》Let A(1,-2), B(3,6),C(5,y) and D(x,2) are the vertices of a parallelogram ABCD

==》.AC and BD are the diagonals.

==》O is the midpoint of AC and BD. If O is the mid-point of AC ,then the coordinates of O are

$\tt \: ( \frac{1 + 5}{2} \times \frac{ - 2 + y}{2} ) = ( \frac{6}{2}, \frac{ - 2 + y}{2} )$

==》if O is the mid point of BD then coordinates of O are

$\bf \: ( \frac{x + 3}{2} \times \frac{2 + 6}{2} ) = ( \frac{x + 3}{2}, \frac{8}{2} )$

==》since both coordinates are of the same point O

$\fcolorbox{red}{rd}{Therefore }$

$\tt \: \frac{6}{2} = \frac{x + 3}{2} \\ \\ \tt \: 6 = x + 3 \\ \\ \tt \: x = 6 - 3 \\ \\ \bf \: x = 3$

$\fcolorbox{red}{rd}{Therefore }$

$\tt \frac{ - 2 + y}{2} = \frac{8}{2} \\ \\ \tt \: - 2 + y = 8 \\ \\ \bf \:y = 8 + 2 \\ \\ \bf y = 10$

$\huge \fcolorbox{red}{rd}{hence }$

$\huge \tt \fcolorbox{gold}{rd}{x = 3 }$

$\huge \tt \fcolorbox{green}{rd}{y = 10 }$

$\huge \tt \fcolorbox{green}{red}{be \: brainly }$

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