The vertices of $\Delta ABC$ are $A(2, 4)$,$B(5, 0)$,and $C(5, 4)$. Then the area of $\Delta ABC = \ldots$

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

For $A(0, 0)$ and $B(4, 8)$,$M$ is the midpoint of $\overline{AB}$ and $N$ is the midpoint of $\overline{BM}$,then the coordinates of $N$ are.........

If the distance between the points $(2, -2)$ and $(-1, x)$ is $5$,one of the values of $x$ is

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 $km$.

The coordinates of the point which is equidistant from the three vertices of the $\triangle AOB$ as shown in the figure are