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Q25.

Expert-verified

Algebra 2

Found in: Page 415

Book edition Middle English Edition

Author(s) Carter

Pages 804 pages

ISBN 9780079039903

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Short Answer

Find the distance between the pair of points with the given coordinates $(1, - 14) and (- 6, 10)$ .

The distance between the given pair of points is $25 units$ .

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Write down the given information.

The given pair of points have coordinates $(1, - 14) and (- 6, 10)$ .

Step 2. Concept used.

If a line segment has end-points at $(x_{1}, y_{1}) and (x_{2}, y_{2})$ then the distance $(d)$ between these points is given as:

$|d| = \sqrt{{(x_{2} - x_{1})}^{2} + {(y_{2} - y_{1})}^{2}} .... (1)$

Step 3. Calculation.

The distance $(d)$ between the pair of points with given coordinates $(1, - 14) and (- 6, 10)$ is evaluated using the formula (1) stated above.

\begin{matrix} |d| = \sqrt{{(x_{2} - x_{1})}^{2} + {(y_{2} - y_{1})}^{2}} \\ = \sqrt{{(- 6 - 1)}^{2} + {(10 + 14)}^{2}} \\ = \sqrt{{(- 7)}^{2} + {(24)}^{2}} \\ = 25 units \end{matrix}

Step 4. Conclusion.

The distance between the given pair of points is $25 units$ .

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