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

Name the type of quadrilateral formed,if any,by the following points,and give reasons for your answer: $(-3, 5), (3, 1), (0, 3), (-1, -4)$.

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.

Determine if the points $(1,5), (2,3),$ and $(-2,-11)$ are collinear.

The vertices of a $\Delta ABC$ are $A(4, 6)$,$B(1, 5)$,and $C(7, 2)$. $A$ line is drawn to intersect sides $AB$ and $AC$ at $D$ and $E$ respectively,such that $\frac{AD}{AB} = \frac{AE}{AC} = \frac{1}{4}$. Calculate the area of $\Delta ADE$ and compare it with the area of $\Delta ABC$.

Show that the points $(1,7), (4,2), (-1,-1)$ and $(-4,4)$ are the vertices of a square.