સમાંતર બાજુ ચ્તુષ્કોણની બે બાજુ 4 x+5 y=0 અને | vedclass

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Question

Both the lines pass through origin.

point $D$ is equal of intersection of $4 x+5 y=0\,  \,11 x+7 y=9$

So, coordinates of point $D=\left(\fr

Vedclass · Accepted Answer

$(2,2)$

Vedclass · Answer

Both the lines pass through origin.

point $D$ is equal of intersection of $4 x+5 y=0\,  \,11 x+7 y=9$

So, coordinates of point $D=\left(\frac{5}{3},-\frac{4}{3}\right)$

Also, point $B$ is point of intersection of $7 x+2 y=0\, \, 11 x+7 y=9$

So, coordinates of point $B=\left(-\frac{2}{3}, \frac{7}{3}\right)$

diagonals of parallelogram intersect at middle let middle point of $B,D$

$\Rightarrow\left(\frac{\frac{5}{3}-\frac{2}{3}}{2}, \frac{-4}{3}+\frac{7}{3}\right)=\left(\frac{1}{2}, \frac{1}{2}\right)$

equation of diagonal $AC$

$\Rightarrow(y-0)=\frac{\frac{1}{2}-0}{\frac{1}{2}-0}(x-0)$

$y=x$

diagonal $AC$ passes through $(2,2)$

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