coordinates

Two sides of a square are consecutively based upon two straight lines $6\times x - 8\times y + 5 = 0$ and $3\times x - 4 \times y + 10 = 0$. Find the area of this square.

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$6x-8y+5=0\\ f(x)=\frac{3}{4}x+0.625\\ 3x-4y+10=0\\ g(x)=\frac{3}{4}x+2.5$

$y=mx+n\\ m_{f,g}=0.75$

$\alpha =arctan(m)$

$A=a^2\\ a= (g(0)-f(0))\cdot cos(\alpha)\\ a =(g(0)-f(0))\cdot cos(arctan(m))\\ a =(2.5-0.625)\cdot cos(arctan(0.75))=\color{blue}1.5$

$A=[(2.5-0.625)\cdot cos(arctan(0.75))]^2$

$A=2.25$

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