Find the coordinates of the point which divides the line segment joining the points $(4, -3)$ and $(8, 5)$ in the ratio $3: 1$ internally.

Name the type of quadrilateral formed,if any,by the following points,and give reasons for your answer: $(4,5), (7,6), (4,3), (1,2)$.

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 $D$.

Find the area of the triangle whose vertices are (in square units): $(-5,-1), (3,-5), (5,2)$.

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?

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.