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

If $(1, 2), (4, y), (x, 6)$ and $(3, 5)$ are the vertices of a parallelogram taken in order,find $x$ and $y$.

Find the area of the quadrilateral whose vertices,taken in order,are $(-4,-2), (-3,-5), (3,-2),$ and $(2,3)$ (in square units).

Find the ratio in which the $y$-axis divides the line segment joining the points $(5, -6)$ and $(-1, -4)$. Also,find the point of intersection.

In each of the following,find the value of $k$ for which the points are collinear: $(7, -2), (5, 1), (3, k)$.

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. Taking $A$ as origin,find the coordinates of the vertices of the triangle.