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Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 9: Q. 20 (page 621)

Find the distance from $P_{1}$ to $P_{2}$ .
role="math" localid="1646776682625" $P_{1} = (2, - 3, - 3) a n d P_{2} = (4, 1, - 1)$

Short Answer

Expert verified

The distance between points $P_{1} = (2, - 3, - 3) a n d P_{2} = (4, 1, - 1)$ is $2 \sqrt{6}$

Step by step solution

01

Step 1. Given data

The given points are

$P_{1} (x_{1}, y_{1}, z_{1}) = (2, - 3, - 3) P_{2} (x_{2}, y_{2}, z_{2}) = (4, 1, - 1)$

02

Step 2. Distance between points

Use distance formula

$d (P_{1}, P_{2}) = \sqrt{{(x_{2} - x_{1})}^{2} + {(y_{2} - y_{1})}^{2} + {(z_{2} - z_{1})}^{2}} d (P_{1}, P_{2}) = \sqrt{{(4 - 2)}^{2} + {(1 - (- 3))}^{2} + {(- 1 - (- 3))}^{2}} d (P_{1}, P_{2}) = \sqrt{4 + 16 + 4} d (P_{1}, P_{2}) = \sqrt{24} d (P_{1}, P_{2}) = 2 \sqrt{6}$

so the distance between points is $2 \sqrt{6}$

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