Question

3 multiple choice 1 point a sequence of transformations was applied to an equilateral triangle in a coordinate plane. the transformations used were rotations, reflections, and translations. which statement about the resulting figure is true? it may be an obtuse triangle with at least one side the same length as the original triangle. it may be a scalene triangle, and all the side lengths may differ from the original triangle. it must be an equilateral triangle, but the side lengths may differ from the original triangle. it must be an equilateral triangle with the same side lengths as the original triangle.

Explanation:

1. Recall the properties of rotations, reflections, and translations (rigid transformations): These transformations preserve the shape and size of a figure.
2. Analyze each option:

• Option 1: Rigid transformations preserve angle measures. An equilateral triangle has all angles \(60^\circ\), so it can't become obtuse (obtuse has an angle \(> 90^\circ\)). Eliminate.
• Option 2: Rigid transformations preserve side lengths, so side lengths can't all differ. Also, an equilateral triangle can't become scalene (scalene has all sides of different lengths). Eliminate.
• Option 3: Rigid transformations preserve side lengths, so side lengths can't differ. Eliminate.
• Option 4: Rotations, reflections, and translations are rigid transformations. They preserve the shape (so it remains equilateral) and size (so side lengths are the same as the original). This is correct.

Answer:

D. It must be an equilateral triangle with the same side lengths as the original triangle. (Assuming the last option is D; if the options were labeled A - D in order, the correct one is the last option as analyzed.)