Find the coordinates of the point which divides the line segment joining the points $(-1, 7)$ and $(4, -3)$ in the ratio $2:3$.

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

Find a relation between $x$ and $y$ if the points $(x, y), (1, 2)$ and $(7, 0)$ are collinear.

Find the area of a rhombus if its vertices are $(3,0), (4,5), (-1,4)$ and $(-2,-1)$ taken in order. (in square units)

Find the distance between the following pairs of points: $(-5, 7)$ and $(-1, 3)$. (in $\sqrt{2}$)