For what value of $y$ does the triangle with vertices $A(2, 7)$,$B(4, y)$,and $C(-2, 6)$ form a right angle at $A$?

Let a point $A$ lie between the parallel lines $L_1$ and $L_2$ such that its distances from $L_1$ and $L_2$ are $6$ and $3$ units, respectively. Then the area (in sq. units) of the equilateral triangle $ABC$, where the points $B$ and $C$ lie on the lines $L_1$ and $L_2$ respectively, is:

If $A(1,3)$ and $C(7,5)$ are two opposite vertices of a square,then find the equation of a side passing through $A$.

Which one of the following statements is true?

$A$ line $4x+y=1$ passes through the point $A(2,-7)$ and meets the line $BC$,whose equation is $3x-4y+1=0$,at the point $B$. The equation of the line $AC$ such that $AB=AC$ is

The point $(-4, 5)$ is a vertex of a square and one of its diagonals lies along the line $7x - y + 8 = 0$. The equation of the other diagonal is: