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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→A'

And

M:B→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.

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Most popular questions from this chapter

When the word MOM is reflected in a vertical line, the image is still MOM. Can you think of the other words that are unchanged when reflected in a vertical line?

If fx=x2+1, find f3 and f-3. Is f a one-to-one function?

Under a reflection, is an angle mapped to a congruent angle? Is a polygon always mapped to a polygon with the same area? Explain.

In each exercise Rk:A→A'. Find an equation of line k.

For each transformation given:

  1. Plot the three points A0,4, B4,6, and C2,0 and their images A', B', and C' under the transformation.
  2. State whether the transformation appears to be an isometry.
  3. Find the pre image of 12,6.

H:x,y→-x,-y
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