Question

Parallelogram is shown with vertices at negative 5 comma 1, negative 4 comma 3, negative 1 comma 3, and negative 2 comma 1. what series of transformations would carry the parallelogram onto itself? (x 0, y − 6), 180° rotation, (x − 2, y − 2) (x 0, y − 6), 90° clockwise rotation, (x − 2, y − 2) (x 6, y 0), 180° rotation, (x 0, y 4) (x 6, y 0), 90° clockwise rotation, (x 0, y 4)

Answer 1

The correct transformation series to map the parallelogram onto itself is a 180° rotation around the central point of the parallelogram, followed by a suitable translation, if necessary.

Step-by-step explanation:

You asked which series of transformations would carry a parallelogram onto itself given the vertices at (-5, 1), (-4, 3), (-1, 3), and (-2, 1). A parallelogram can be mapped onto itself by a 180° rotation around the center or by a translation that moves the parallelogram but keeps its orientation and shape the same. To find the correct transformation, we need to establish the center of the parallelogram. In this case, the central point of the parallelogram can be found by averaging the x-coordinates and the y-coordinates of the vertices, which gives us the point (-3, 2). The transformation (x 0, y − 6), 180° rotation, (x − 2, y − 2) is not correct because a translation of (x 0, y − 6) would move the parallelogram vertically down and not map it onto itself. Similarly, a 90° clockwise rotation wouldn't map the parallelogram onto itself since the orientation would change. However, a 180° rotation around the center point followed by an appropriate translation that moves the parallelogram back to its original position, may work.