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

If $(-4,3)$ and $(4,3)$ are two vertices of an equilateral triangle,find the coordinates of the third vertex,given that the origin lies in the interior of the triangle.

If the distance between $(3, a)$ and $(4, 1)$ is $\sqrt{10},$ then the value of $a$ is $ \ldots \ldots \ldots \ldots .$

Ayush starts walking from his house to his office. Instead of going to the office directly,he goes to a bank first,from there to his daughter's school,and then reaches the office. What is the extra distance travelled by Ayush in reaching his office (in $, km$)? (Assume that all distances covered are in straight lines).
If the house is situated at $(2,4)$,the bank at $(5,8)$,the school at $(13,14)$,and the office at $(13,26)$,where coordinates are in $km$.

In which ratio and at which point does the $Y$-axis divide the line segment joining $A (-2, 4)$ and $B (1, 1)$ from $A$?

If $d[(5,0), (x, 4)] = \sqrt{17}$,then $x = \ldots \ldots \ldots$