Chapter 10: Q16. (page 661)

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

Short Answer

Expert verified

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

Step by step solution

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 $(3, 5)$ iswidth="26">5units.

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

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

Short Answer

Step by step solution

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

Step 2. Calculate the distance.

Step 3. State the conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Probability and Statistics

Decision Maths

Geometry

Statistics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

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

Short Answer

Step by step solution

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

Step 2. Calculate the distance.

Step 3. State the conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Probability and Statistics

Decision Maths

Geometry

Statistics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

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