Question

#1 a square with a side length of 4 units is rotated 30° about 1 vertex and then the square is translated 2 units left. which option best describes the the resulting image?
a rhombus
b rectangle
c square
d parallelogram

Explanation:

1. Recall the properties of rotations and translations: Both rotation and translation are rigid transformations. Rigid transformations preserve the shape and size of a figure.
2. A square, when rotated about a vertex (a rigid transformation) and then translated (another rigid transformation), will retain all its original properties. The side lengths remain equal (4 units), and all angles remain \(90^\circ\) because rigid transformations do not change side lengths or angle measures.
3. A square is a special case of a rhombus (all sides equal), rectangle (all angles \(90^\circ\)), and parallelogram (opposite sides parallel and equal). But since the transformations are rigid, the resulting figure is still a square as all defining properties (equal sides, right angles) are preserved.

Answer:

C. Square