Q7. - Algebra 2

Question

Find the distance between the pair of points $\left(7,8\right)\text{ and }\left(-4,9\right)$ with the given coordinates.

Step-by-Step Solution

Answer

The distance between the given pair of points is $\sqrt{122}\text{ units}$.

Step 1. Write down the given information.

The given pair of points have coordinates $\left(7,8\right)\text{ and }\left(-4,9\right)$.

Step 2. Concept used.

If a line segment has end-points at $\left(x_1,y_1\right)\text{ and }\left(x_2,y_2\right)$ then the distance $\left(d\right)$ 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 $\left(7,8\right)\text{ and }\left(-4,9\right)$ is evaluated using the formula (1) stated above.

$\begin{array}{c}\left|d\right|=\sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2}\\ =\sqrt{{\left(-4-7\right)}^2+{\left(9-8\right)}^2}\\ =\sqrt{{\left(-11\right)}^2+{\left(1\right)}^2}\\ =\sqrt{122}\text{ units}\end{array}$

Step 4. Conclusion.

The distance between the given pair of points is $\sqrt{122}\text{ units}$.