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Q. 12

Expert-verified

Geometry

Found in: Page 532

Book edition Student Edition

Author(s) Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen

Pages 227 pages

ISBN 9780395977279

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Short Answer

Find the slope and length of AB.
A(3, -1), B(5, -7)

The slope of the line is -3 and the length of the line is $2 \sqrt{10}$ units.

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step-1 – Given

The given points are A(3, -1) and B(5, -7).

Step-2 – To determine

We have to find the slope and the length of the line $\bar{A B}$ .

Step-3 – Calculation

We will use the slope formula with two points $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ :

$m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$

The given points are A(3, -1) and B(5, -7).

$m = \frac{- 7 - (- 1)}{(5) - (3)} = \frac{- 6}{2} = - 3$

Length of the line $\bar{A B}$ :

$\sqrt{{(x_{2} - x_{1})}^{2} + {(y_{2} - y_{1})}^{2}} = \sqrt{{(5 - 3)}^{2} + {(- 7 - (- 1))}^{2}} = 2 \sqrt{10}$

So, the slope of the line is -3 and the length of the line is $2 \sqrt{10}$ units.

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