If two opposite vertices of a square are $(5, -4)$ and $(-3, 2)$,find its area.

In a $\triangle ABC$,$AB = AC = 37$. Let $D$ be a point on $BC$ such that $BD = 7$ and $AD = 33$. The length of $CD$ is:

Suppose $ABCD$ is a trapezium whose sides and height are integers and $AB$ is parallel to $CD$. If the area of $ABCD$ is $12$ and the sides are distinct,then $|AB-CD|$ is:

Let the circumcentre of a triangle with vertices $A(a, 3)$,$B(b, 5)$,and $C(a, b)$,where $ab > 0$,be $P(1, 1)$. If the line $AP$ intersects the line $BC$ at the point $Q(k_{1}, k_{2})$,then $k_{1} + k_{2}$ is equal to.

The diagonal passing through the origin of a quadrilateral formed by $x = 0, y = 0, x + y = 1$ and $6x + y = 3$ is

The area of the triangle formed by the lines $y = m_1x + c_1$,$y = m_2x + c_2$ and $x = 0$ is: