If the distance between $A(1, 3)$ and $B(a, 0)$ is $3$ units,then $a = \ldots$

Find a point on the $y$-axis which is equidistant from the points $A(6, 5)$ and $B(-4, 3)$.

The distance between the points $(6, 8)$ and $(3, 4)$ is .........

In $\Delta ABC$,if $A(b, c)$,$B(-a, 0)$,and $C(a, 0)$,and $D$ is the midpoint of $\overline{BC}$,then prove that $AB^2 + AC^2 = 2(AD^2 + BD^2)$.

The Class $X$ students of a secondary school in Krishinagar have been allotted a rectangular plot of land for their gardening activity. Saplings of Gulmohar are planted on the boundary at a distance of $1\, m$ from each other. There is a triangular grassy lawn in the plot as shown in the Figure. The students are to sow seeds of flowering plants on the remaining area of the plot. Taking $A$ as origin,find the coordinates of the vertices of the triangle.

Name the type of quadrilateral formed,if any,by the following points,and give reasons for your answer: $(-3, 5), (3, 1), (0, 3), (-1, -4)$.