Question

A polygon with vertices (2, 3) and (2, 5) and (4, 3) is reflected across the y-axis and then rotated 90° counter-clockwise about the origin. After these transformations will the shape still be similar to the original? Why?

Answer 1

After a reflection across the y-axis and a counter-clockwise rotation, the polygon's vertices change position but the shape remains similar because reflections and rotations are rigid transformations that preserve shape and size.

Step-by-step explanation:

The question asks whether a polygon with given vertices will remain similar to the original shape after a reflection across the y-axis followed by a 90° counter-clockwise rotation about the origin. To determine this, we first need to reflect the given points across the y-axis, which means we change the sign of the x-coordinates of the points while keeping the y-coordinates the same; the reflected vertices become (-2, 3), (-2, 5), and (-4, 3). Next, a 90° counter-clockwise rotation about the origin will switch the coordinates of each point and change the sign of the new x-coordinate. After performing the rotation, our vertices become (3, 2), (5, 2), and (3, 4).

After these transformations, the distances between corresponding points in the polygon and the angles between the sides remain the same, although the orientation and position of the polygon have changed. Therefore, the transformed polygon is still similar to the original polygon because similarity is maintained through reflections and rotations, which are rigid transformations that preserve shape and size.