Area of a Triangle and Quadrilateral

Show that the points $(-2, 5), (6, -1) \text{and} (2, 2)$ are collinear.

Find the inclination of a line $y=2$.

If the area of the triangle is $0$, then the given points are called

Find the value of $k$ if the points $P(2, 3), Q(4, k)$ and $R(6, –3)$ are collinear.

Point $P$ divides line $AB$, with $A\left(5,14\right)$ and $B\left(7,16\right)$ in ratio $3:2$ externally. Find the coordinates of $P$.

Point $P$ divides line $AB$, with $A\left(2,3\right)$ and $B\left(5,6\right)$ in ratio $3:2$ externally. Find the coordinates of $P$.

Point $P$ divides line $AB$, with $A\left(7,6\right)$ and $B\left(5,10\right)$ in ratio $3:2$ externally. Find the coordinates of $P$.

Point $P$ divides line $AB$, with $A\left(5,4\right)$ and $B\left(8,6\right)$ in ratio $3:2$ externally. Find the coordinates of $P$.

Point $P$ divides line $AB$, with $A\left(3,4\right)$ and $B\left(7,12\right)$ in ratio $3:2$ externally. Find the coordinates of $P$.

Calculate the area of a triangle with vertices $(1,1),(3,1)$ and $(5,7)$.

If points $(1,2),(-1, x)$ and $(2,3)$ are collinear, then $x$ will be :

If the vertices of a triangle have integral coordinates, the triangle cannot be