If one of the sides of a square is `3x-4y-12=0` and the center is `(0,0)` , then find the equations of the diagonals of the square.

Monjur Alahi

If one of the sides of a square is `3x-4y-12=0` and the center is `(0,0)` , then find the equations of the diagonals of the square.


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Salim Ahmed Kawsar

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The diagonals of square are inclined at an angle of `45^(@)` with the sides.
Slope of the line 3x-4y-12 = 0 is 3/4.
Let the slope of the diagonal be m. Then,
`tan 45^(@) = |(m-(3//4))/(1+(3//4)m)|`
`therefore 4+3m = +-(4m-3)`
or 4+3m = 4m-3 or 4+3m=3-4m
or m = 7 or m `=(-1)/(7)`
Therefore, the equations of diagonals are 7x-y = 0 and x+7y = 0.

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