For the triangle with vertices $A (6, 7),$ $B (-2, 3)$ and $C (9, 1),$ find the coordinates of the point on $\overline{BC}$ where the bisector of $\angle A$ intersects $\overline{BC}$.

If $A(0, 0)$,$B(2, 0)$,$C(2, 2)$,and $D(0, 2)$,then $\square ABCD$ is a $\ldots \ldots \ldots$

If $P (0,0), Q (0,5)$ and $R (6,0),$ then $\Delta PQR$ is $\ldots \ldots \ldots$ triangle.

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

Show that $A(1, 4)$,$B(7, -2)$,and $C(9, 6)$ are the vertices of an isosceles triangle.

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 $km$.