If the area of the triangle formed by the vertices $A(-1, 2), B(k, -2)$ and $C(7, 4)$ (taken in order) is $22$ sq. units, find the value of $k$.

If the points $P\left(-1, -4\right), Q\left(b, c\right)$ and $R\left(5, -1\right)$ are collinear and $2b+c=4$, then find the values of $b$ and $c$.

The floor of a hall is covered with identical tiles which are in the shapes of triangles. One such triangle has the vertices $(-3, 2), (-1, -1)$ and $(1, 2)$. If the floor of the hall is completely covered by $110$ tiles, find the area of the floor.

The given diagram shows a plan for constructing a new parking lot at a campus. It is estimated that such construction would cost $₹1300$ per square feet. What will be the total cost for making the parking lot?

Find the slope of a line joining the given points

$\left(-6, 1\right)$ and $\left(-3, 2\right)$

Find the slope of a line joining the given points

$\left(-\frac{1}{3}, \frac{1}{2}\right)$ and $\left(\frac{2}{7}, \frac{3}{7}\right)$