Chapter 14.1, Problem 11WE

(a)

To determine

To find: The mapping is one to one mapping of $l_1$ and $l_2$ .

Answer to Problem 11WE

The mapping is one-to-one mapping of $l_1\text{}\text{and}{l}_2$ .

Explanation of Solution

Given information:

The given diagram is shown below.

  

Calculation:

In the diagram, $P\text{'}$ is called the image of $P$ , and $P$ is called pre image of $P\text{'}$ . The diagram shows the images of two points $P\text{and}Q$ on the line $l_1\text{and }{l}_2$ .

It is given that mapping $M$ maps each point $P\text{of}{l}_1$ to the point $P\text{'}$ by writing:

  $M:P\to P\text{'}$

Thus the mapping is one-to-one mapping of $l_1\text{and}{l}_2$ as, the line is joining one point at a line

Therefore, the mapping is one-to-one mapping of $l_1\text{}\text{and}{l}_2$ .

(b)

To determine

To find: This mapping preserve or distort distance.

Answer to Problem 11WE

The mapping preserve distance as line $l_1\text{and}{l}_2$ are parallel.

Explanation of Solution

Given information:

The given diagram is shown below.

  

Calculation:

In the above diagram it shows that the line $l_1\text{and}{l}_2$ are parallel. So the line $l_1\text{and}{l}_2$ will never meet if extended.

Thus, the mapping preserve distance.

Therefore, the mapping preserve distance as line $l_1\text{and}{l}_2$ are parallel.

(c)

To determine

To find: The mapping preserve distance when line $l_1\text{and}{l}_2$ were not parallel.

Answer to Problem 11WE

The mapping cannot preserve distance because $l_1\text{and}l$ are not parallel.

Explanation of Solution

Given information:

If line $l_1\text{and}{l}_2$ were not parallel.

Calculation:

When the line $l_1\text{and}{l}_2$ were not parallel then the diagram that will be formed is like this

  

From the above diagram it is clear shown, If line $l\text{and}{l}_2$ would not parallel then they would be meeting at a certain points that is $O\text{'}$ .

So the mapping cannot preserve distance because $l_1\text{and}l$ are not parallel.

Therefore, the mapping cannot preserve distance because $l_1\text{and}l$ are not parallel.