Question

HELPPPPPP MATH TEST DUE IN 1 HOUR!!!!

The vertices of △ABC are (1, 2), (3, 2), and (2, 7), respectively. A sequence of transformations maps △ABC to △DEF. The vertices of △DEF are (3, −6), (5, −6), and (4, −1), respectively.

Is the sequence of transformations mapping △ABC to △DEF an isometry?

Responses

No. The sequence of transformations is an isometry because it contains only rigid transformations.
No. The sequence of transformations is an isometry because it contains only rigid transformations.

Yes. The sequence of transformations is an isometry because it contains only non-rigid transformations.
Yes. The sequence of transformations is an isometry because it contains only non-rigid transformations.

No. The sequence of transformations is an isometry because it contains only non-rigid transformations.
No. The sequence of transformations is an isometry because it contains only non-rigid transformations.

Yes. The sequence of transformations is an isometry because it contains only rigid transformations.

Answer 1

An isometry is a transformation that preserves distances and angles. Rigid transformations, which include translation, rotation, and reflection, are types of transformations that preserve distances and angles. Non-rigid transformations, such as stretching or shearing, do not preserve distances and angles.

You've mentioned the options and the correct one is:

No. The sequence of transformations is an isometry because it contains only rigid transformations.

This means that the sequence of transformations from △ABC to △DEF includes only rigid transformations, which maintain the distances and angles between the points.

Answer 2

The correct answer is:

No. The sequence of transformations is NOT an isometry because it contains only non-rigid transformations.

Step-bye step explanation

An isometry is a transformation that preserves distances and angles between points. Rigid transformations, such as translations, rotations, and reflections, are examples of isometries because they do not change the shape or size of the figure.

In this case, the given sequence of transformations maps triangle ABC to triangle DEF. However, the sequence contains only non-rigid transformations, which means that the shape and size of the triangle change.

The transformation from (1, 2) to (3, -6) involves both a translation and a vertical stretch, which is a non-rigid transformation. Similarly, the transformations from (3, 2) to (5, -6) and from (2, 7) to (4, -1) also involve non-rigid transformations.

Since the sequence of transformations contains only non-rigid transformations, it is not an isometry.