Question

Talia is playing with a plastic hoop that she spins around her waist. The spinning hoop resembles a(1 point)
Responses

dilation.
dilation.

translation.
translation.

reflection.
reflection.

rotation.△EFG is rotated −90 degrees (clockwise) to create △XYZ . Which of the following statements must be true?(1 point)Which graph demonstrates a transformation that preserves both distance and angle measure?(1 point)

Answer 1

The spinning hoop that Talia is using resembles a **rotation** because it is spinning around a central point (her waist).

Regarding the second part of your question, if triangle \( \triangle EFG \) is rotated \( -90 \) degrees (clockwise) to create \( \triangle XYZ \), then it must be true that corresponding angles of the two triangles are congruent and the lengths of corresponding sides are equal. In simpler terms, the two triangles are similar but not congruent unless they started as the same triangle before the rotation.

Lastly, for the statement about transformations that preserve both distance and angle measure, we are generally referring to isometric transformations. The transformations that preserve distance and angle measure include **translations**, **rotations**, and **reflections**. Each of these transformations maintains the shape and size of the figure.

If you have a specific graph in mind for the last part, please provide more details or share the graphs, and I can help you determine which one maintains both distance and angle measure.