Q16. - Algebra 1

Question

Find the distance between the points with the given coordinate.

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

Step-by-Step Solution

Answer

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

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.

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

Step 3. State the conclusion.

Therefore, distance between the points $(2,3)$ and $(3,5)$ is width="26" style="max-width: none; vertical-align: -4px;" $\sqrt{5}$ units.