Assam Board Solutions for Chapter: Coordinate Geometry, Exercise 1: Exercise 7.1

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: $\left(\mathrm{a},\mathrm{b}\right),\left(-\mathrm{a},-\mathrm{b}\right)$

Name the type of quadrilateral formed, if any, by the following points, and give reasons for your answer.

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

Name the type of quadrilateral formed, if any, by the following points, and give reasons for your answer:

$\left(4,\mathrm{}5\right),\mathrm{}\left(7,\mathrm{}6\right),\mathrm{}\left(4,\mathrm{}3\right),\mathrm{}\left(1,\mathrm{}2\right)$

Find the point on the $x-$axis which is equidistant from $\left(2,\mathrm{}-5\right)$ and $\left(-2,\mathrm{}9\right)$.

Find the values of $y$ for which the distance between the points $\mathrm{}\mathrm{P}\left(2,\mathrm{}-3\right)$ and $\mathrm{}\mathrm{Q}(10,\mathrm{}y)$ is $\mathrm{}10\mathrm{}$ units.

If $\mathrm{}\mathrm{Q}\left(0,\mathrm{}1\right)$ is equidistant from $\mathrm{}\mathrm{P}\left(5,\mathrm{}-3\right)$ and $\mathrm{}\mathrm{R}\left(x,\mathrm{}6\right)$, find the values of $x$. Also find the distances $\mathrm{}\mathrm{Q}\mathrm{R}$ and $\mathrm{}\mathrm{P}\mathrm{R}$.

Find a relation between $x$ and $y$ such that the point $\left(x,\mathrm{}y\right)$ is equidistant from the point $\left(3,\mathrm{}6\right)$ and $\left(-3,\mathrm{}4\right)$.