Question

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

Short answer

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

Step-by-step solution

Step 1. Given Information.

It is given that $ABCD$ is trapezoid.

Step 2. Explanation.

It is given that $ABCD$ is trapezoid and each point of $DC$ is mapped by using similar parallel measurements to the side $AD$.Then the mapping is one-to-one mapping.

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

Step 3. Conclusion.

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