/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q21. Mapping M maps points A and B to... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 14: Q21. (page 576)

Mapping M maps points A and B to the same image point. Explain why the mapping M does not preserve distance.

Short Answer

Expert verified

The mapping does not preserve distance.

Step by step solution

01

Step 1. Given Information.

It is given that mapping M maps points A and B to the same image point.

02

Step 2. Explanation.

A mapping from set A to set B is called a one-to-one mapping if every number of B has exactly one pre-image in A.

Now consider A' is the image of the point A and B' is the image of point B.

M:A鈫�A'

And

M:B鈫�B'

As the points are at different locations therefore the length of AB will be greater than the zero.

AB>0

But as mapping M maps points Aand B to the same image point, the length of the line A'B'will be equal to zero.

A'B'=0

03

Step 3. Conclusion.

Therefore, the mapping does not preserve distance.

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.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

If a transformation maps two parallel lines to two image lines that are also parallel, we say that parallelism is invariant under the transformation. Is parallelism invariant under a reflection?

Copy each figure on graph paper. Then draw the image by reflection in line k.

Points A-D are reflected in the x-axis. Points E-H are reflected in the y-axis. State the coordinates of the images.

Explain how Corollary I follows from Theorem 14-1.

Consider the mapping S:x,y鈫�x,0.

  1. Plot the points P4,5,Q-3,2, and R-3,-1 and their images.
  2. Does S appear to be an isometry? Explain.
  3. Is S a transformation? Explain.
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Discrete Mathematics

Read Explanation

Calculus

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Mechanics Maths

Read Explanation

Pure Maths

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.