If one of the diagonals of a square is along he line x $$=$$ $$2y$$ and one of its vertices is (3$$, $$0), then its side through this vertex nearer to the origin is given by the equation

Question

If one of the diagonals of a square is along  he line x $$=$$ $$2y$$ and one of its vertices is (3$$, $$0), then its side through this vertex nearer to the origin is given by the equation

Infinity Learn · Accepted Answer

The point (3$$, $$0) does not lie on the diagonal x $$=$$ $$2y$$. Let the equation of a side through the vertex (3$$, $$0) be $$y-0=m(x-3)Since$$ the angle between a side and a diagonal of a square is π$$/4$$ we have±$$tan$$$$π$$$$4=m-1/21+m(1/2)=2m-12+m$$⇒  $$m=3$$,$$-1/3Thus$$ the equation of a side through (3$$, $$0) $$isy=3(x-3)$$ or $$y=-13(x-3)$$ and the one nearer to the  origin is $$3y$$ $$+$$ x –$$3$$ $$=$$ $$0$$

If one of the diagonals of a square is along he line $x = 2 y$ and one of its vertices is (3, 0), then its side through this vertex nearer to the origin is given by the equation

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If one of the diagonals of a square is along he line x = 2y and one of its vertices is (3, 0), then its side through this vertex nearer to the origin is given by the equation

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If one of the diagonals of a square is along he line $x = 2 y$ and one of its vertices is (3, 0), then its side through this vertex nearer to the origin is given by the equation