Find the value of $k$ if the points $A(2, 3)$,$B(4, k)$,and $C(6, -3)$ are collinear.

Find the coordinates of the points which divide the line segment joining $A (-2, 2)$ and $B (2, 8)$ into four equal parts.

Let $A(4,2)$,$B(6,5)$,and $C(1,4)$ be the vertices of $\Delta ABC$. The median from $A$ meets $BC$ at $D$. Find the coordinates of the point $D$.

In what ratio does the point $(-4, 6)$ divide the line segment joining the points $A(-6, 10)$ and $B(3, -8)$?

Let $A(4, 2), B(6, 5)$ and $C(1, 4)$ be the vertices of $\Delta ABC$. Find the coordinates of the centroid of the triangle.

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?