Log In Start studying!

Select your language

Suggested languages for you:

Americas

English (US)

Europe

Q16.

Expert-verified

Algebra 1

Found in: Page 661

Book edition Student Edition

Author(s) Carter, Cuevas, Day, Holiday, Luchin

Pages 801 pages

ISBN 9780078884801

Answers without the blur.

Just sign up for free and you're in.

Register for Free I’ll do it later

Short Answer

Find the distance between the points with the given coordinate.
$(2, 3), (3, 5)$

The distance between the coordinates $(2, 3)$ and $(3, 5)$ is $\sqrt{5}$ units.

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. State the concept of ‘Distance between two points in 2 dimensional plane’.

Let the two points in 2 dimensional plane be $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ .

The distance between the points is given as:

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

Where $d$ is the distance.

Step 2. Calculate the distance.

The two points which is given are $(2, 3)$ and $(3, 5)$ .

Substitute $(2, 3)$ as $(x_{1}, y_{1})$ and $(3, 5)$ as $(x_{2}, y_{2})$ in $(1)$ to calculate the distance.

localid="1647926325268" $\begin{array}{l} d = \sqrt{{(x_{2} - x_{1})}^{2} + {(y_{2} - y_{1})}^{2}} \\ = \sqrt{{(3 - 2)}^{2} + {(5 - 3)}^{2}} \\ = \sqrt{{(1)}^{2} + {(2)}^{2}} \\ = \sqrt{1 + 4} \\ = \sqrt{5} \end{array}$

Step 3. State the conclusion.

Therefore, distance between the points $(2, 3)$ and $(3, 5)$ is width="26" style="max-width: none; vertical-align: -4px;" $\sqrt{5}$ units.

Most popular questions for Math Textbooks

Solve each equation. Check your solution.

$\sqrt{a + 4} = 6$

Graph the function, and compare to the parent graph. State the domain and range.

$y = 3 \sqrt{x}$

The length of the side of a square is given by the function $s = \sqrt{A}$ , where $A$ is the area of the square. What is the length of the side of a square that has an area of 121 square inches?

A 121 inches

B 11 inches

C 44 inches

D 10 inches

Which of the following sets of measures could not be the sides of a right triangle?

$A$ $(12, 16, 24)$ $C$ $(24, 45, 51)$

$B$ $(10, 24, 26)$ $D$ $(18, 24, 30)$

Graph the function, and compare to the parent graph. State the domain and range.

$g (x) = 4 \sqrt{x}$

Want to see more solutions like these?

Sign up for free to discover our expert answers

Get Started - It’s free

Recommended explanations on Math Textbooks

94% of StudySmarter users get better grades.

Sign up for free