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

What is the ratio of the area of $\triangle PQS$ to the area of $\triangle PQR$?

Area of the rhombus bounded by the four lines,$ax \pm by \pm c = 0$ is :

Let $A(1, 1)$,$B(-4, 3)$,and $C(-2, -5)$ be the vertices of a triangle $ABC$. Let $P$ be a point on the side $BC$,and let $\Delta_{1}$ and $\Delta_{2}$ be the areas of triangle $APB$ and triangle $ABC$,respectively. If $\Delta_{1} : \Delta_{2} = 4 : 7$,then find the area enclosed by the lines $AP$,$AC$,and the $x$-axis.

The number of triangles formed by the lines $x-y+3=0$,$2x-y+3=0$,$3x-y+2=0$,and $x+y-3=0$ is:

The coordinates of the vertices $P, Q, R$ and $S$ of a square $PQRS$ inscribed in the triangle $ABC$ with vertices $A \equiv (0, 0)$,$B \equiv (3, 0)$,and $C \equiv (2, 1)$,given that two of its vertices $P$ and $Q$ lie on the side $AB$,are respectively: