Chapter 11: Q. 11.6 (page 1073)

Use the Distance Formula to find the distance between the points $(- 2, - 5)$ and $(- 3, - 4)$ . Write the answer in exact form and then find the decimal approximation, rounded to the nearest tenth if needed.

Short Answer

Expert verified

The distance between the points in exact form is $\sqrt{2}$ and its decimal approximation is $1.4$ .

Step by step solution

Step 1. Definition

The distance between two points $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ is given by the distance formula as

$d = \sqrt{{(x_{2} - x_{1})}^{2} + {(y_{2} - y_{1})}^{2}}$

Step 2. Substitute the values in the formula

To find the distance between the points $(- 2, - 5)$ and $(- 3, - 4)$ , substitute $- 2$ for $x_{1}$ , $- 5$ for $y_{1}$ , $- 3$ for $x_{2}$ , and $- 4$ for $y_{2}$ in the distance formula and simplify.

$d = \sqrt{{(x_{2} - x_{1})}^{2} + {(y_{2} - y_{1})}^{2}} d = \sqrt{(- 3 - {(- 2))}^{2} + (- 4 - {(- 5))}^{2}} d = \sqrt{{(- 1)}^{2} + 1^{2}} d = \sqrt{1 + 1} d = \sqrt{2}$

As it is not a perfect square so it can be approximated as $d \approx 1.4$ .

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Use the Distance Formula to find the distance between the points $(- 2, - 5)$ and $(- 3, - 4)$ . Write the answer in exact form and then find the decimal approximation, rounded to the nearest tenth if needed.

Short Answer

Step by step solution

Step 1. Definition

Step 2. Substitute the values in the formula

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Use the Distance Formula to find the distance between the points (-2,-5) and (-3,-4). Write the answer in exact form and then find the decimal approximation, rounded to the nearest tenth if needed.

Short Answer

Step by step solution

Step 1. Definition

Step 2. Substitute the values in the formula

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Discrete Mathematics

Mechanics Maths

Statistics

Pure Maths

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Use the Distance Formula to find the distance between the points $(- 2, - 5)$ and $(- 3, - 4)$ . Write the answer in exact form and then find the decimal approximation, rounded to the nearest tenth if needed.