Chapter 10: Q...1 (page 667)

The distance $d$ from $P_{1} = (3, - 4)$ to $P_{2} = (- 2, 1)$ is $d =___________$

Short Answer

Expert verified

The distance between the points $P_{1} = (3, - 4)$ and $P_{2} = (- 2, 1)$ is $5 \sqrt{2}$ .

Step by step solution

Step 1. Given Informmation

The given two points are $P_{1} = (3, - 4)$ and $P_{2} = (- 2, 1)$ .

Step 2. Aim of the problem

Here, we need to find the distance between the points $P_{1} = (3, - 4)$ and $P_{2} = (- 2, 1)$

Step 3. Concept

The formula to find the distance between the points $P_{1} = (x_{1}, y_{1})$ and $P_{2} = (x_{2}, y_{2})$ is:

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

Step 4. Finding the distance between the points using the distance formula

The distance between the points $P_{1} = (3, - 4)$ and $P_{2} = (- 2, 1)$ is,

localid="1647084625539" $d = \sqrt{{(x_{2} - x_{1})}^{2} + {(y_{2} - y_{1})}^{2}} d = \sqrt{{(- 2 - 3)}^{2} + (1 - {(- 4))}^{2}} d = \sqrt{{(- 5)}^{2} + {(5)}^{2}} d = \sqrt{25 + 25} d = \sqrt{50} d = \sqrt{25 \times 2} d = 5 \sqrt{2}$

Therefore, the distance between the two given points is $5 \sqrt{2}$ .

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.

The distance $d$ from $P_{1} = (3, - 4)$ to $P_{2} = (- 2, 1)$ is $d =___________$

Short Answer

Step by step solution

Step 1. Given Informmation

Step 2. Aim of the problem

Step 3. Concept

Step 4. Finding the distance between the points using the distance formula

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Logic and Functions

Decision Maths

Theoretical and Mathematical Physics

Geometry

Probability and Statistics

Study anywhere. Anytime. Across all devices.

The distance dfrom P1=(3,-4)to P2=(-2,1)is d=___________

Short Answer

Step by step solution

Step 1. Given Informmation

Step 2. Aim of the problem

Step 3. Concept

Step 4. Finding the distance between the points using the distance formula

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Logic and Functions

Decision Maths

Theoretical and Mathematical Physics

Geometry

Probability and Statistics

Study anywhere. Anytime. Across all devices.

The distance $d$ from $P_{1} = (3, - 4)$ to $P_{2} = (- 2, 1)$ is $d =___________$