Question

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

Short answer

The mapping does not preserve distance.

Step-by-step solution

Step 1. Given Information.

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

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 $A\text{'}$ is the image of the point A and $B\text{'}$ is the image of point B.

$M:A\to A\text{'}$

And

$M:B\to B\text{'}$

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 $A\text{'}B\text{'}$will be equal to zero.

$A\text{'}B\text{'}=0$

Step 3. Conclusion.

Therefore, the mapping does not preserve distance.