Find the distance between the following pairs of points:
$\left(2,3\right),\left(4,1\right)$

 

Find the distance between the following pair of points.

$\left(-5,7\right), \left(-1,3\right)$

Find the distance between the pair of points: $\left(\mathrm{a},\mathrm{b}\right),\left(-\mathrm{a},-\mathrm{b}\right)$

In a classroom, $\mathrm{}4$ friends are seated at the points $\mathrm{}\mathrm{A},\mathrm{}\mathrm{B},\mathrm{}\mathrm{C}$ and $\mathrm{}\mathrm{D}$ as shown in Fig. Champa and Chameli walk into the class and after observing for a few minutes Champa asks Chameli, “Don’t you think $\mathrm{}\mathrm{A}\mathrm{B}\mathrm{C}\mathrm{D}$ is a square?” Chameli disagrees.

Using 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.

$\mathrm{A}=\left(-3,5\right),\mathrm{B}=\left(3,1\right),\mathrm{C}=\left(0,3\right),\mathrm{D}=\left(-1,-4\right)$