If one of the diagonals of a square is along the line $$x=2y$$ and one of its vertices is (3$$, $$0), then its sides through this vertex are given by the equations

Question

If one of the diagonals of a square is along the line $$x=2y$$ and one of its vertices is (3$$, $$0), then its sides through this vertex are given by the equations

Infinity Learn · Accepted Answer

Clearly the point (3$$, $$0) does not lie on the diagonal $$x=2$$ y.Let m be the slope of a side passing through (3$$, $$0). Then,its equation $$isy-0=m(x-3)$$.                                  (i)Since$$ the angle between a diagonal and a side of a square· isπ$$/4$$. Therefore, angle between $$x=2y$$ and y−$$0=m(x$$−$$3) isalso π$$/4$$. Consequently, we havetan⁡π$$4=$$±m−$$1/21+m/2$$⇒$$m=3$$,−$$13Substituting$$ the values of min (i), we $$obtainy-3x+9=0$$ and $$3y+x-3=0$$ as the required sides.

If one of the diagonals of a square is along the line $x = 2 y$ and one of its vertices is (3, 0), then its sides through this vertex are given by the equations

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If one of the diagonals of a square is along the line x=2y and one of its vertices is (3, 0), then its sides through this vertex are given by the equations

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Ready to Test Your Skills?

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If one of the diagonals of a square is along the line $x = 2 y$ and one of its vertices is (3, 0), then its sides through this vertex are given by the equations