$P(3, 2)$ and $Q(7, k)$ are the given points. If $d(P, Q) = 5$,then $k = \dots \dots \dots$

Find the point on the $X$-axis which is equidistant from $(5, 4)$ and $(-2, 3)$.

The distance of the point $P$ on the $X-$axis from $A(11, 12)$ is $13$ units. The coordinates of $P$ are $\ldots \ldots \ldots \ldots$.

If two of the vertices of an equilateral triangle are $(0,0)$ and $(3, \sqrt{3}),$ find the coordinates of the third vertex.

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 $km$.

State whether the following statements are true or false. Justify your answer.
Points $A(4,3), B(6,4), C(5,-6)$ and $D(-3,5)$ are the vertices of a parallelogram.