Q8. - Algebra 2

Question

Find the distance between the pair of points $\left(0.5,1.4\right)\text{ and }\left(1.1,2.9\right)$with the given coordinates.

Step-by-Step Solution

Answer

The distance between the given pair of points is$\sqrt{2.61}\text{ units}$.

Step 1. Write down the given information.

The given pair of points have coordinates$\left(0.5,1.4\right)\text{ and }\left(1.1,2.9\right)$.

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 $\left(0.5,1.4\right)\text{ and }\left(1.1,2.9\right)$ is evaluated using the formula (1) stated above.

$\begin{array}{c}\left|d\right|=\sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2}\\ =\sqrt{{\left(1.1-0.5\right)}^2+{\left(2.9-1.4\right)}^2}\\ =\sqrt{{\left(0.6\right)}^2+{\left(1.5\right)}^2}\\ =\sqrt{2.61}\\ =1.615\text{ units}\mathrm{....}\left(\text{Approx.}\right)\end{array}$

Step 4. Conclusion.

The distance between the given pair of points is $\sqrt{2.61}\text{ units}$.