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Q. 12

Expert-verifiedFound in: Page 532

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.

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

We have to find the slope and the length of the line$\overline{AB}$ .

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.

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