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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 11: Q. 6 (page 1069)

In the following ecercises,find the distance between the points.Write the answer in exact form and the find the decimal approximation,rounded the nearest tenth if needed.
$(- 1, 3)$ and $(5, - 5)$

Short Answer

Expert verified

The distance is $d = 10$

Step by step solution

01

Step 1.Given information

Consider the given points $(- 1, 3) a n d (5, - 5)$

The distance formula states that the distance $d$ between points $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ is $d = \sqrt{{(x_{2} - x_{1})}^{2} + {(y_{2} - y_{1})}^{2}}$

02

Step 2.First lable the points as

$(x_{1}, y_{1}) = (- 1, 3) a n d (x_{2}, y_{2}) = (5, - 5)$ .

Now substitute $x_{1}, y_{1}, x_{2} a n d y_{2}$ values in the distance formula.

localid="1667916127572" $d = \sqrt{(5 - {(- 1))}^{2} + {(- 5 - 3)}^{2}}$

03

Step 3.Now simplify the radical as shown as below

$d = \sqrt{{(6)}^{2} + (- 8})^{2} = \sqrt{36 + 64} = \sqrt{100} = 10$

Therefore the distance $d = 10$

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