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Q25.

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Found in: Page 415

### Algebra 2

Book edition Middle English Edition
Author(s) Carter
Pages 804 pages
ISBN 9780079039903

# Find the distance between the pair of points with the given coordinates$\left(1,-14\right)\text{and}\left(-6,10\right)$.

The distance between the given pair of points is $25\text{units}$.

See the step by step solution

## Step 1. Write down the given information.

The given pair of points have coordinates $\left(1,-14\right)\text{and}\left(-6,10\right)$.

## 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 $\left(1,-14\right)\text{and}\left(-6,10\right)$ is evaluated using the formula (1) stated above.

$\begin{array}{c}\left|d\right|=\sqrt{{\left({x}_{2}-{x}_{1}\right)}^{2}+{\left({y}_{2}-{y}_{1}\right)}^{2}}\\ =\sqrt{{\left(-6-1\right)}^{2}+{\left(10+14\right)}^{2}}\\ =\sqrt{{\left(-7\right)}^{2}+{\left(24\right)}^{2}}\\ =25\text{units}\end{array}$

## Step 4. Conclusion.

The distance between the given pair of points is $25\text{units}$.