If the points $(-5, 1), (p, 5)$ and $(10, 7)$ are collinear,then the value of $p$ will be

Let $a, b, c$ be the side-lengths of a triangle and $l, m, n$ be the lengths of its medians. Put $K = \frac{l+m+n}{a+b+c}$. Then,as $a, b, c$ vary,$K$ can assume every value in the interval

The equations of the sides $AB$,$BC$,and $CA$ of a triangle $ABC$ are $2x + y = 0$,$x + py = 15a$,and $x - y = 3$ respectively. If its orthocentre is $(2, a)$,where $-\frac{1}{2} < a < 2$,then $p$ is equal to...

Let $B$ and $C$ be two points on the line $y+x=0$ such that $B$ and $C$ are symmetric with respect to the origin. Suppose $A$ is a point on the line $y-2x=2$ such that $\triangle ABC$ is an equilateral triangle. Then,the area of the $\triangle ABC$ is

The area (in square units) of the triangle formed by the lines $x=0, y=0$ and $3x+4y=12$ is:

If the points $(1, 1)$,$(-1, -1)$,and $(-\sqrt{3}, k)$ are the vertices of an equilateral triangle,then what is the value of $k$?