Find the area of the triangle whose vertices are (in square units): $(-5,-1), (3,-5), (5,2)$.

Find the area of the triangle formed by joining the mid-points of the sides of the triangle whose vertices are $(0,-1), (2,1)$ and $(0,3)$. Find the ratio of this area to the area of the given triangle.

Find the coordinates of the point which divides the line segment joining the points $(4, -3)$ and $(8, 5)$ in the ratio $3: 1$ internally.

If $A (-5, 7)$,$B (-4, -5)$,$C (-1, -6)$,and $D (4, 5)$ are the vertices of a quadrilateral,find the area of the quadrilateral $ABCD$ (in square units).

The Class $X$ students of a secondary school in Krishinagar have been allotted a rectangular plot of land for their gardening activity. Saplings of Gulmohar are planted on the boundary at a distance of $1\, m$ from each other. There is a triangular grassy lawn in the plot as shown in the Figure. The students are to sow seeds of flowering plants on the remaining area of the plot.
What will be the coordinates of the vertices of $\Delta PQR$ if $C$ is the origin?
Also,calculate the area of the triangle in this case.

Name the type of quadrilateral formed,if any,by the following points,and give reasons for your answer: $(-1,-2), (1,0), (-1,2), (-3,0)$.