Distance Between Any Two Points

Show that $\left(4, 3\right)$ is the centre of the circle passing through the points $\left(9, 3\right),\left( 7, -1\right), \left(-1, 3\right)$. Also find its radius.

Let $A\left(2, 2\right), B\left(8, -4\right)$ be two given points in a plane. If a point $P$ lies on the $X$- axis (in positive side), and divides $AB$ in the ratio $1:2$, then find the coordinates of $P$.

Find the value of '$a$' such that $PQ=QR$ where $P, Q$, and $R$ are the points whose coordinates are $\left(6, -1\right), \left(1, 3\right)$ and $\left(a, 8\right)$ respectively.

Calculate the distance between the points $A\left(7, 3\right)$ and $B$ which lies on the $x$-axis whose abscissa is $11$.

Show that the points $A\left(-4, -3\right), B\left(3, 1\right), C\left(3, 6\right), D\left(-4, 2\right)$ taken in that order form the vertices of a parallelogram.

Show that the points $A\left(7, 10\right), B\left(-2, 5\right), C\left(3, -4\right)$ are the vertices of a right angled triangle.

Show that the following points $A\left(3, 1\right), B\left(6, 4\right)$ and $C\left(8, 6\right)$ lies on a straight line.

Find the distance between the points $\left(-4, 3\right), \left(2, -3\right)$.

Find the distance (in $\mathrm{units}$) between the pair of points.

$\left(3,-9\right)$ and $\left(-2,3\right)$

Find the distance (in $\mathrm{units}$) between the pair of points.

$\left(\mathrm{a},\mathrm{b}\right)$ and $\left(\mathrm{c},\mathrm{b}\right)$

Find the distance (in $\mathrm{units}$) between the pair of points.

$\left(3,4\right)$ and $\left(-7,2\right)$

Find the distance (in $\mathrm{units}$) between the pair of points.

$\left(1,2\right)$ and $\left(4,3\right)$

Let $A(2,3)$ and $B(2,-4)$ be two points. If $P$ lies on the $x$-axis, such that $AP=\frac{3}{7}AB$. Find the coordinates of $P$.

If $(1,-2),(3,6),(x, 10)$ and $(3,2)$ are the vertices of the parallelogram taken in order, then the value of $x$ is

The distance between the point $(5,-1)$ and the origin is

If ${\mathrm{Q}}_1,{\mathrm{Q}}_2,{\mathrm{Q}}_3,{\mathrm{Q}}_4$ are the quadrants in a Cartesian plane then ${\mathrm{Q}}_2\cap {\mathrm{Q}}_3$is

If $(x+2,4)=(5, y-2),$ then the coordinates $(x, y)$ are

If the points $A(2,0), B(-6,0), C(3, a-3)$ lie on the $x-$axis then the value of $a$ is

The distance between the two points $(2,3)$ and $(1,4)$ is

The radius of a circle with centre at origin is $30$ units. Write the coordinates of the points where the circle intersects the axes. Find the distance between any two such points.