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Answers without the blur. Sign up and see all textbooks for free! Q. 12

Expert-verified Found in: Page 532 ### Geometry

Book edition Student Edition
Author(s) Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen
Pages 227 pages
ISBN 9780395977279 # 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.

See the step by step solution

## 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$\overline{AB}$ .

## Step-3 – Calculation

We will use the slope formula with two points$\left({x}_{1},{y}_{1}\right)$ and$\left({x}_{2},{y}_{2}\right)$ :

$m=\frac{{y}_{2}-{y}_{1}}{{x}_{2}-{x}_{1}}$

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

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

Length of the line$\overline{AB}$ :

$\sqrt{{\left({x}_{2}-{x}_{1}\right)}^{2}+{\left({y}_{2}-{y}_{1}\right)}^{2}}=\sqrt{{\left(5-3\right)}^{2}+{\left(-7-\left(-1\right)\right)}^{2}}=2\sqrt{10}$

So, the slope of the line is -3 and the length of the line is$2\sqrt{10}$ units. ### Want to see more solutions like these? 