Find the values of $y$ for which the distance between the points $P(2, -3)$ and $Q(10, y)$ is $10$ units.

If the distance between $A(-4, -3)$ and $B(6, a)$ is $10$,then $a = \ldots \ldots \ldots . . .$

Using the distance formula,show that the points $(0, -3), (1, -1),$ and $(2, 1)$ are collinear.

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 $km$.

If the distance between points $A(a, 2)$ and $B(3, -5)$ is $\sqrt{53},$ find the possible values of $a$.

If $P (2, -3)$ and $Q (7, 9)$,then the length of $\overline{PQ}$ is ...........