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

Find the point on the $x$-axis which is equidistant from $(2, -5)$ and $(-2, 9).$

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

Find the area of the triangle whose vertices are $(2, 3), (-1, 0),$ and $(2, -4)$.

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

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.