Question

Find the distance between the points with the given coordinate.

$\mathbf{(}\mathbf{-}\mathbf{1}\mathbf{,}\mathbf{-}\mathbf{1}\mathbf{)}\mathbf{,}\mathbf{(}\mathbf{3}\mathbf{,}\mathbf{2}\mathbf{)}$

Short answer

The distance between the coordinates$(-1,-1)$ and$(3,2)$is5 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 $(-1,-1)$and $(3,2)$.

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

$\begin{array}{l}d=\sqrt{{(x_2-x_1)}^2+{(y_2-y_1)}^2}\\ =\sqrt{{(3-(-1))}^2+{(2-(-1))}^2}\\ =\sqrt{{(3+1)}^2+{(2+1)}^2}\\ =\sqrt{{\left(4\right)}^2+{\left(3\right)}^2}\\ =\sqrt{16+9}\\ =\sqrt{25}\\ =5\end{array}$

Step 3. State the conclusion.

Therefore, distance between the points$(-1,-1)$ and $(3,2)$is 5 units.