Question

Find the distance between the points with the given coordinate.

$\mathbf{(}\mathbf{2}\mathbf{,}\mathbf{3}\mathbf{)}\mathbf{,}\mathbf{(}\mathbf{3}\mathbf{,}\mathbf{5}\mathbf{)}$

Short answer

The distance between the coordinates $(2,3)$and $(3,5)$ is$\sqrt{5}$units.

Step-by-step solution

Step 1. State the concept of ‘Distance between two points in 2 dimensional plane’.

Let the two points in 2 dimensional plane be $(x_1,y_1)$and $(x_2,y_2)$.

The distance between the points is given as:

$d=\sqrt{{(x_2-x_1)}^2+{(y_2-y_1)}^2}\dots \left(1\right)$

Where $d$is the distance.

Step 2. Calculate the distance.

The two points which is given are $(2,3)$and $(3,5)$.

Substitute $(2,3)$as $(x_1,y_1)$and $(3,5)$as $(x_2,y_2)$in $\left(1\right)$to calculate the distance.

localid="1647926325268" $\begin{array}{l}d=\sqrt{{(x_2-x_1)}^2+{(y_2-y_1)}^2}\\ =\sqrt{{(3-2)}^2+{(5-3)}^2}\\ =\sqrt{{\left(1\right)}^2+{\left(2\right)}^2}\\ =\sqrt{1+4}\\ =\sqrt{5}\end{array}$

Step 3. State the conclusion.

Therefore, distance between the points$(2,3)$and $(3,5)$iswidth="26">5units.