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  • If one of the diagonals of a square is along the lineand one of its vertices 

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

Option: 1

\mathrm{y-3 x+9=0,3 y+x-3=0}


Option: 2

\mathrm{y+3 x+9=0,3 y+x-3=0}


Option: 3

\mathrm{y-3 x+9=0,3 y-x+3=0}


Option: 4

\mathrm{y-3 x+3=0,3 y+x+9=0}


Answers (1)

best_answer

Diagonal of the square is along

\mathrm {x=2y} ----------(1)

The point (3, 0) does not lie on (1).

Let the side through this vertex be  \mathrm {\mathrm{y}-0=m(x-3)}

Angle between side (2) and diagonal (1) is 45°.

\mathrm {\therefore \quad \tan ^{-1} \frac{m-1 / 2}{1+m \cdot(1 / 2)}= \pm 45^{\circ} \quad \Rightarrow m=3,-1 / 3}

from (2), the required sides are

 \mathrm {y-3 x+9=0} and \mathrm {3 y+x-3=0},  which are given in (a).

 

Posted by

Ritika Kankaria

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