<u>Answer:</u>
1 cm : 10.5 km
<u>Step-by-step explanation:</u>
We are given that two towns are 31.5 km in real and are 3 cm apart on a map and we are to find the scale of the map.
For this, we can use the ratio method.
Therefore, the scale of the map would be 1 cm : 10.5 km.
The best explanation for why the rotation is isometric is "<u>The rectangle did not change shape or size</u>". Hence the <u>second option</u> is the right choice.
There are four main categories of transformations:
A stiff transformation known as an isometry maintains perimeter and area while also preserving length and angle measurements. In other words, there is congruence between the preimage and the image. Translations, reflections, and rotations are therefore isometric, but dilations are not since the image and preimage are comparable, rather than congruent figures.
The transformation in the question will be isometric when the preimage of the rectangle before 360° rotation, will be congruent to the image after the rotation.
The congruency is best described by the option "The rectangle did not change shape or size", as that is the basis of congruency.
Thus, the best explanation for why the rotation is isometric is "<u>The rectangle did not change shape or size</u>". Hence the <u>second option</u> is the right choice.
Learn more about isometric transformations at
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