Show that the points $A(5, 6), B(1, 5), C(2, 1)$ and $D(6,2)$ are the vertices of a square.

Prove that the points $A(0, 1), B(1, 4), C(4, 3), D(3, 0)$ are the vertices of a square.

If the point $(x, y)$ is equidistant from the point $(a+b, b-a)$ and $(a-b, a+b)$, prove that $bx=ay$.

If the point on $x-$axis, which is equidistant from $(-2,5)$ and $(2,-3)$ is $\left(\mathrm{a},0\right)$, then find the value of $\mathrm{a}$.

If the point on the $y-$axis which is equidistant from $(-5, -2)$ and $(3, 2)$ is $(0, k)$, find the value of $k$.

If the distance between the two points $(b+c, c+a)$ and $(c+a, a+b)$ is $\sqrt{a^2+x{b}^2+c^2-yab-2bc}$. Find $x$

Prove that the points $(6, 9), (0, 1)$ and $(-6, -7)$ are collinear.