Find the lengths of the medians of the triangle whose vertices are $(1, -1), (0, 4)$ and $(-5, 3)$

Find the centroid of the triangle formed by the straight lines $x-2y=0$, $x+y=3$ and $2x+y+4=0$.

Show that the middle point of the hypotenuse of a right-angled triangle is equidistant from the vertices.

Find the co-ordinates of the incentre of the triangle, whose vertices are $(0, 6)$, $(8, 12)$ and $(8, 0)$.

Find the area of triangle formed by the points $(3, 4), (2, -1)$ and $(4, -6)$.

If the area of triangle formed by the points $(a, c+a), (a, c)$ and $(-a, c-a)$ is $k^2 \mathrm{sq}. \mathrm{units}$ then find $k$.

Show that following points are collinear:

$(1, -1), (2, 1)$ and $(4, 5)$

Show that following points are collinear:

$(-5, 1), (5, 5)$ and $(10, 7)$

For what value of $x$ will the following lie on a line:

$(x, -1), (5, 7), (8, 11)$