Chapter 14: Q13. (page 575)

ABCDis a trapezoid. Describe a way of mapping each point of $\bar{D C}$ to a point of $\bar{A B}$ so that the mapping is one-to-one. Is your mapping an isometry?

Short Answer

Expert verified

The mapping is one-to-one mapping and it is not isometry.

Step by step solution

Step 1. Given Information.

It is given that $A B C D$ is trapezoid.

Step 2. Explanation.

It is given that $A B C D$ is trapezoid and each point of $D C$ is mapped by using similar parallel measurements to the side $A D$ .Then the mapping is one-to-one mapping.

No, the mapping will not be isometry because the distance between the pre images, $A and B$ is larger than the distance between their corresponding images, $D and C$ .

Step 3. Conclusion.

Therefore, the mapping is one-to-one mapping and it is not isometry.

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ABCDis a trapezoid. Describe a way of mapping each point of $\bar{D C}$ to a point of $\bar{A B}$ so that the mapping is one-to-one. Is your mapping an isometry?

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Explanation.

Step 3. Conclusion.

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ABCDis a trapezoid. Describe a way of mapping each point of DC¯ to a point of AB¯ so that the mapping is one-to-one. Is your mapping an isometry?

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Step by step solution

Step 1. Given Information.

Step 2. Explanation.

Step 3. Conclusion.

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ABCDis a trapezoid. Describe a way of mapping each point of $\bar{D C}$ to a point of $\bar{A B}$ so that the mapping is one-to-one. Is your mapping an isometry?