Chapter 11: Q. 11.1 (page 1071)

Use the rectangular coordinate system to find the distance between the points $(6, 1)$ and $(2, - 2)$ .

Short Answer

Expert verified

The distance between the given points is $5$ .

Step by step solution

Step 1. Plot the points

Plot the two points. Connect the two points with a line and then draw a right triangle.

Step 2. Find the lengths

Find the length of each leg.

The rise is three units and the run is four units. So the right triangle can be shown as

Step 3. Use Pythagorean Theorem

Use the Pythagorean Theorem, $a^{2} + b^{2} = c^{2}$ , to find $d$ , the distance between the two points.

Substitute $3$ for $a$ , $4$ for $b$ , and $d$ for $c$ we get

$\begin{array}{rcl} 3^{2} + 4^{2} & = & d^{2} \\ 9 + 16 & = & d^{2} \\ 25 & = & d^{2} \end{array}$

Step 4. Solve for d

As $d^{2} = 25$ , so using the square root property we get

$d = \pm \sqrt{25} d = \pm 5$

But the value of distance cannot be negative, so we eliminate $d = - 5$ .

So the distance between the points is role="math" localid="1645188625093" $d = 5$ .

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.

Use the rectangular coordinate system to find the distance between the points $(6, 1)$ and $(2, - 2)$ .

Short Answer

Step by step solution

Step 1. Plot the points

Step 2. Find the lengths

Step 3. Use Pythagorean Theorem

Step 4. Solve for d

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Theoretical and Mathematical Physics

Calculus

Logic and Functions

Geometry

Pure Maths

Study anywhere. Anytime. Across all devices.

Use the rectangular coordinate system to find the distance between the points (6,1) and (2,-2).

Short Answer

Step by step solution

Step 1. Plot the points

Step 2. Find the lengths

Step 3. Use Pythagorean Theorem

Step 4. Solve for d

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Theoretical and Mathematical Physics

Calculus

Logic and Functions

Geometry

Pure Maths

Study anywhere. Anytime. Across all devices.

Use the rectangular coordinate system to find the distance between the points $(6, 1)$ and $(2, - 2)$ .