Find the area of the triangle whose vertices are $(2, 3), (-1, 0),$ and $(2, -4)$.

If the points $A (6, 1)$,$B (8, 2)$,$C (9, 4)$,and $D (p, 3)$ are the vertices of a parallelogram,taken in order,find the value of $p$.

Find the value of $k$ for which the points $(8,1), (k,-4),$ and $(2,-5)$ are collinear.

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.

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

Find the area of a triangle whose vertices are $(1, -1), (-4, 6)$ and $(-3, -5)$ (in square units).