Question

are the two figures congruent? if so, describe a sequence of transformations that maps one figure onto the other figure. if not, explain why they are not congruent. chose the correct answer and justification. no, they are not congruent. no sequence of rotations, reflections, and/or translations matches the two figures up exactly. yes, they are congruent. rotating polygon duck 2 units down and 4 units left maps polygon duck onto polygon bear. yes, they are congruent. rotating polygon duck 180° clockwise about the origin maps polygon duck onto polygon bear. yes, they are congruent. reflecting polygon duck across the y - axis and then reflecting the image across the x - axis maps polygon duck onto polygon bear

Explanation:

Step1: Recall congruence definition

Two figures are congruent if one can be mapped onto the other by a sequence of rotations, reflections, and translations.

Step2: Analyze rotation

Rotating polygon DUCK 180° clock - wise about the origin changes the sign of both x and y - coordinates of each vertex. By observing the grid and the orientation of the polygons, we can see that rotating polygon DUCK 180° clockwise about the origin maps polygon DUCK onto polygon BEAR.

Step3: Check other options

Moving 2 units down and 4 units left is a translation which won't map DUCK onto BEAR. Reflecting across the y - axis and then the x - axis won't map DUCK onto BEAR either. And clearly, there is a way to map them onto each other, so they are congruent.

Answer:

Yes, they are congruent. Rotating polygon DUCK 180° clockwise about the origin maps polygon DUCK onto polygon BEAR.