Find the distance between the points $A(5, 8)$ and $B(1, 2)$.

$A(5,2), B(3,4)$ and $C(x, y)$ are collinear and $AB = BC$,then the coordinates of $C$ are...............

Find the area of the triangle $ABC$ with vertex $A (1, -4)$ and the mid-points of the sides passing through $A$ being $(2, -1)$ and $(0, -1)$ (in $sq. units$).

Students of a school are standing in rows and columns in their playground for a drill practice. $A, B, C$ and $D$ are the positions of four students as shown in the figure. Is it possible to place Jaspal in the drill in such a way that he is equidistant from each of the four students $A, B, C$ and $D$? If so,what should be his position?

$A(6,1), B(8,2)$ and $C(9,4)$ are three vertices of a parallelogram $ABCD$. If $E$ is the midpoint of $DC$,find the area of $\triangle ADE$ (in sq. units).

Prove that $(2a, 4a)$, $(2a, 6a)$, and $(2a + \sqrt{3}a, 5a)$ are the vertices of an equilateral triangle.