Question

three vertices of a parallelogram in order are (1,2) (2,4) and (3,7). Find the fourth vertex

Answer 1

$<b><i>Three vertices of parallelogram in order A(1,2) , B(2,4) , C(3,7)$

$<b><u>Let 4th vertex be D(x,y):$

$\large\sf\implies\: midpoint \:of\: A(1,2)\: and \:C(3,7)\: is$

$\large\sf\implies\: midpoint\:=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$

$\large\sf\implies\:midpoint\:=(\frac{1+3}{2},\frac{2+7}{2})$

$\large\sf\implies\:midpoint\:=(2,\frac{9}{2})$

$\large\sf\:midpoint\: of \: B(2,4)\: and \:D(x,y)\: is$

$\large\sf\implies\: midpoint\:=(\frac{2+x}{2},\frac{4+y}{2})$

$\textsf{\orange{4th vertex is equal to mid point of AC and mid point of BD}}$

$\large\sf\implies\:(2,\frac{9}{2})\:=(\frac{2+x}{2},\frac{4+y}{2})$
________________________________________
$\large\sf\frac{2+x}{2}\:=\:2$

x=2 and y=5

(x,y)=(2,5)