The opposite vertices of a square are $(1, 2)$ and $(3, 8)$, then the equation of a diagonal of the square passing through the point $(1, 2)$, is

One side of a rectangle lies along the line $4x + 7y + 5 = 0.$ Two of its vertices are $(-3, 1)$ and $(1, 1)$. Then the equations of other three sides are

Two consecutive sides of a parallelogram are $4x + 5y = 0$ and $7x + 2y = 0$. If the  equation to one diagonal is $11x + 7y = 9$, then the equation to the other diagonal is :-

The vertex of a right angle of a right angled triangle lies on the straight line $2x + y - 10 = 0$ and the two other vertices, at points $(2, -3)$ and $(4, 1)$ then the area of triangle in sq. units is

Three lines $x + 2y + 3 = 0 ; x + 2y - 7 = 0$ and $2x - y - 4 = 0$ form the three sides of two squares. The equation to the fourth side of each square is

The co-ordinates of the vertices $A$ and $B$ of an isosceles triangle $ABC (AC = BC)$ are $(-2,3)$ and $(2,0)$ respectively. $A$ line parallel to $AB$ and having a $y$ -intercept equal  to $\frac{43}{12}$ passes through $C$, then the co-ordinates of $C$ are :-