Question

Find the distance between the pair of points with the given coordinates $\left(2\sqrt{3},-5\right)\text{and}\left(-3\sqrt{3},9\right)$.

Short answer

The distance between the given pair of points is$\sqrt{271}\text{units}$.

Step-by-step solution

Step 1. Write down the given information.

The given pair of points have coordinates $\left(2\sqrt{3},-5\right)\text{and}\left(-3\sqrt{3},9\right)$.

Step 2. Concept used.

If a line segment has end-points at$\left(x_1,y_1\right)\text{and}\left(x_2,y_2\right)$the distance between these points is given as:

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

Step 3. Calculation.

The distance $\left(d\right)$ between the pair of points with given coordinates$\left(2\sqrt{3},-5\right)\text{and}\left(-3\sqrt{3},9\right)$ is evaluated using the formula (1) stated above.

$\begin{array}{c}\left|d\right|=\sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2}\\ =\sqrt{{\left(-3\sqrt{3}-2\sqrt{3}\right)}^2+{\left(9+5\right)}^2}\\ =\sqrt{75+196}\\ =\sqrt{271}\text{units}\end{array}$

Step 4. Conclusion.

The distance between the given pair of points is $\sqrt{271}\text{units}$$\sqrt{271}\text{units}$.