Find the distance between the following pairs of points: $(2,3)$ and $(4,1)$.

Find the ratio in which the $y$-axis divides the line segment joining the points $(5, -6)$ and $(-1, -4)$. Also,find the point of intersection.

Determine if the points $(1,5), (2,3),$ and $(-2,-11)$ are collinear.

To conduct Sports Day activities,in your rectangular shaped school ground $ABCD,$ lines have been drawn with chalk powder at a distance of $1 \,m$ each. $100$ flower pots have been placed at a distance of $1 \,m$ from each other along $AD,$ as shown in the figure. Niharika runs $\frac{1}{4}$ th the distance $AD$ on the $2^{nd}$ line and posts a green flag. Preet runs $\frac{1}{5}$ th the distance $AD$ on the $8^{th}$ line and posts a red flag. What is the distance between both the flags? If Rashmi has to post a blue flag exactly halfway between the line segment joining the two flags,where should she post her flag?

Find the coordinates of a point $A,$ where $AB$ is the diameter of a circle whose centre is $(2,-3)$ and $B$ is $(1,4).$

If $A$ and $B$ are $(-2, -2)$ and $(2, -4)$ respectively,find the coordinates of $P$ such that $AP = \frac{3}{7} AB$ and $P$ lies on the line segment $AB$.