Question

suppose a parallelogram is graphed on a coordinate plane. which series of transformations results in an image that is congruent to its pre - image? select each correct answer. a translation 6.5 units up followed by a translation 0.2 units right a dilation by a factor of 0.7 followed by a 90° clockwise rotation about the origin a 180° rotation about the origin followed by a translation 8 units left a reflection across the x - axis followed by a reflection across the y - axis

Explanation:

1. Translation: Translations (shifting the figure) do not change the size or shape of a figure, so a series of translations will result in a congruent image. A translation 6.5 units up followed by a translation 0.2 units right just moves the parallelogram without altering its size or shape.
2. Dilation: A dilation changes the size of a figure. A dilation by a factor of 0.7 will make the parallelogram smaller, so the resulting image will not be congruent to the pre - image even after a rotation.
3. Rotation and translation: A 180° rotation about the origin changes the orientation of the parallelogram, and a subsequent translation 8 units left just moves it. Rotations and translations are rigid motions that preserve size and shape, so the image is congruent.
4. Reflections: Reflections across the x - axis and y - axis are rigid motions. Each reflection flips the parallelogram over an axis, but they preserve size and shape, so the final image is congruent.

Answer:

a translation 6.5 units up followed by a translation 0.2 units right
a 180° rotation about the origin followed by a translation 8 units left
a reflection across the x - axis followed by a reflection across the y - axis