Question

1. Which of these transformations are isometries? The diagrams are not drawn to scale.

Answer 1

In math, an isometry is a congruent transformation in which the distance (or length) and the angle is preserved or remains the same even after the transformation.

The transformation can be translation, rotation, reflection, etc.

Let us not use this definition of isometry to answer our question, one at a time.

(I) In here, as we can see the distances 10 and 5 and the angle 43 degrees has been preserved. So, this is an isometry.

(II) In here, distances have been halved, so this is not an isometry, even though the angles have been preserved.

(III) In here, the corresponding distances and the angles have been preserved. So, this is an isometry.