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Q. 42

Expert-verified
Found in: Page 15

### Precalculus Enhanced with Graphing Utilities

Book edition 6th
Author(s) Sullivan
Pages 1200 pages
ISBN 9780321795465

# Find the distance $d\left({P}_{1},{P}_{2}\right)$ between the points ${P}_{1}\mathrm{and}{P}_{2}$.${P}_{1}=\left(-4,-3\right);{P}_{2}=\left(6,2\right)$

The distance between the points is $d=5\sqrt{5}$.

See the step by step solution

## Step 1. Given information.

Find the distance between the points.${P}_{1}=\left(-4,-3\right);{P}_{2}=\left(6,2\right)$

## Step 2. Substitute the values in the formula.

The length of the line segment is the distance between the points ${P}_{1}=\left({x}_{1},{y}_{1}\right)=\left(-4,-3\right)\mathrm{and}{P}_{2}=\left({x}_{2},{y}_{2}\right)=\left(6,2\right)$. Using the distance formula with${x}_{1}=-4,{y}_{1}=-3,{x}_{2}=6,\mathrm{and}{y}_{2}=2$, the length d is

$d=\sqrt{{\left({x}_{2}-{x}_{1}\right)}^{2}+{\left({y}_{2}-{y}_{2}\right)}^{2}}\phantom{\rule{0ex}{0ex}}d=\sqrt{{\left(6-\left(-4\right)\right)}^{2}+{\left(2-\left(-3\right)\right)}^{2}}\phantom{\rule{0ex}{0ex}}d=\sqrt{{\left(10\right)}^{2}+{\left(5\right)}^{2}}\phantom{\rule{0ex}{0ex}}d=\sqrt{100+25}\phantom{\rule{0ex}{0ex}}d=\sqrt{125}\phantom{\rule{0ex}{0ex}}d=5\sqrt{5}$

## Step 3. Conclusion.

The distance between the points is $5\sqrt{5}$.