5.1

If $bx+cy=a,$ where $a, b, c$ are of the same sign, be a line such that the area enclosed by the line and the axes of reference is $\frac{1}{8}$ square units, then 

One diagonal of a square is the portion of the line $\sqrt{3}x+y=2\sqrt{3}$ intercepted by the axes. Then an extremity of the other diagonal is

If the coordinates of the vertices of a triangle are rational numbers, then which of the following points of the triangle will always have rational coordinates?

Line $\mathrm{L}$ is perpendicular to the line $5x-y=1$. The area of triangle formed by the line and coordinate axes is $5$. Its equation is

One side of a square of length $a$ is inclined to the $x$-axis at an angle $\alpha$ with one of the vertices of the square at the origin. The equation of a diagonal of the square is

Let the algebraic sum of the perpendicular distances from the points $A\left(2,0\right),B\left(0,2\right),C\left(1,1\right)$to a variable line be zero. Then all such lines

The area of a triangle is $5$ and two of its vertices are $A\left(2,1\right)$ and $B\left(3,-2\right)$. The third vertex which lies on line $y=x+3$ is

If the equations of the hypotenuse and a side of a right-angled isosceles triangle be $x+my=1$ and $x=k$ respectively, then