Distance Formula

Show that $(0,1), (1,2), (2,3)$and $(3,4)$ are collinear.

Show that $(0,2), (1,3), (2,4)$and $(3,5)$ are collinear.

Show that $(1,4), (2,5), (3,6)$and $(4,7)$ are collinear.

Show that $(0,4), (1,6), (2,8)$and $(3,10)$ are collinear.

If the distance of the point $P\left(-5,5\right)$ from the origin is $k\sqrt{2}$ find the value of $k$

Find the distance between the points $P\left(9,-12\right)$ and $Q\left(-6,-4\right)$. 

If the point $(x,y)$ is equidistant from the point $(7,1)$ and point $(3,5)$, then the relation between $x$ and $y$ is $x-y=2$.

The distance between the point $\mathrm{A}(\sin \mathrm{\theta }-\cos \mathrm{\theta }, 0)$ and $\mathrm{B}(0, \sin \mathrm{\theta }+\cos \mathrm{\theta })$ is $\sqrt{2}$.

For what value of $k$, the points $(8,1),(k,-4)$ and $(2,-5)$ are collinear $?$

A point $\mathrm{P}(5, 2)$ is equidistant from the points $(\mathrm{b}, 10)$ and $(0, \mathrm{b})$. Find $\mathrm{b}$.

Find the distance between the origin and the point: $(-15, 8)$

Find the distance between the origin and the point: $(-12, 5)$

Find $a$ if the following points are the vertices of a right triangle with $\angle A=90°$.

$A\left(2, 3\right), B\left(7, a\right), C\left(4, 7\right)$

Find $a$ if the following points are the vertices of a right triangle with $\angle A=90°$.

$A\left(4,3\right), B\left(6,-2\right), C\left(a,-3\right)$

Find the distance between the origin and the point: $(-3, -4)$

Find the distance between the origin and the point:$(-8, 6)$

Calculate the distance between A$(7, 3)$ and B on the $x$-axis, whose abscissa is $11$.

Use graph paper for this question. Take $2 \mathrm{cm}=1 \mathrm{unit}$ on both axes.

Measure and record the distance of the point of intersection of the lines from the origin in cm.

Prove that the points $(1,3), (2,5)$ and $\left(3, 5\right)$ are on the same line.

The distance of the point $\left(-3.-4\right)$ from oringin is