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

Let $A(4, 2)$,$B(6, 5)$,and $C(1, 4)$ be the vertices of $\Delta ABC$. Find the coordinates of points $Q$ and $R$ on medians $BE$ and $CF$ respectively such that $BQ : QE = 2 : 1$ and $CR : RF = 2 : 1$.

In a classroom,$4$ friends are seated at the points $A, B, C$ and $D$ as shown in the figure. Champa and Chameli walk into the class and after observing for a few minutes Champa asks Chameli,"Don't you think $ABCD$ is a square?" Chameli disagrees. Using the distance formula,find which of them is correct.

Name the type of quadrilateral formed,if any,by the following points,and give reasons for your answer: $(-1,-2), (1,0), (-1,2), (-3,0)$.

Find the area of the triangle formed by the points $P(-1.5, 3)$,$Q(6, -2)$,and $R(-3, 4)$ (in square units).

Find the ratio in which the line segment joining the points $(-3, 10)$ and $(6, -8)$ is divided by the point $(-1, 6)$.