Distance between Two Points

The co-ordinates of the points $P$, $Q$ and $S$ are $\left(a{t}^2, 2at\right)$; $\left(\frac{a}{t^2}, \frac{2a}{t}\right)$ and $\left(a, 0\right)$ respectively. Then $\frac{1}{SP}+\frac{1}{SQ}$ is equal to:

If the distance between $\left(4, p\right)$ and $\left(1, 0\right)$ is $5$. Then the value of $p$ is:

Show that the points $(2,-5),(8,1)$ and$(3,-4)$ are collinear.

In the adjoining figure, $ABC$ is an equilateral triangle whose vertex $A$ has the coordinates $(0, \sqrt{3})$. Find the coordinates of $B$ and $C$.

In the given figure, $∆\mathrm{ABC}$ is an equilateral triangle of side $3$ units. Find the co-ordinates of vertex $\mathrm{C}$.

In the given figure, $OABC$is a rectangle. If $l\parallel m$ what is the area of the rectangle $OABC$?

Find the distance of the points $(9, -2)$ from the mid-point of the line segment joining the points $(-3, 2)$ and $(5, 6)$.

If the distance between the points $\left(4, k\right)$ and $\left(1, 0\right)$ is $5$, then what can be the possible values of $k$?

Sridhar calculated the distance between $\mathrm{T}(5, 2)$ and $\mathrm{R}(-4, -1)$ to the nearest tenth is $9.5$ units. Now, you find the distance between $\mathrm{P}(4, 1)$ and $\mathrm{Q}(-5, -2)$. Do you get the same answer that Sridhar got? Why?

Two points $(0,0)$, $\left(3,\sqrt{3}\right)$, makes an equilateral triangle with $3$rd point $P.$ Find that point.

Find $x \text{and} y$co-ordinate of the image of a point $A (2,0)$. $MN$ is plane mirror.

Find the co-ordinates of the point equidistant from the points $A\left(1,2\right),B\left(3,-4\right) \text{and} C\left(5,-6\right)$.

If $O\left(0,0\right); P\left(x,y\right)$ then $OP=?$

Find a point on $x$-axis which is equidistant from the points $(5,-2) \mathit{\text{and}} (-3,2)$

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

Find the distance between the points $\left(3, 1\right)$ and $\left(6, 2\right)$ using distance formula.

The distance of a point $p(x,y)$ from the origin is

Find the area of the quadrilateral formed by the points $(-4,-2),(-3,-5),(3,-2)$ and $(2,3)$

Show that the points are the vertices of a square: $A (3,2), B(0,5), C(-3,2)$ and $D(0,-1)$

Determine whether the points $A (4,5), B (-3,3), C (-6,-13)$, and $D (6,-2)$are the vertices of a kite?