Question

figure a is translated 4 units left and 1 unit down and then reflected over the y - axis. which best explains whether figure b is the image of figure a under the specified transformations? there is not enough information to determine whether figure b is the image of figure a after the transformations. figure b is not the image of figure a because the transformations were performed in an incorrect order. figure b is not the image of figure a because the triangles are not congruent.

Explanation:

Step1: Understand transformation properties

Translation and reflection are rigid transformations. Rigid transformations preserve the shape and size of a figure, meaning the pre - image and image are congruent.

Step2: Analyze the options

• Option 1: Translation and reflection are well - defined transformations. We can check if figure B is the image. So, the statement “There is not enough information” is incorrect.
• Option 2: Transformations (translation and reflection) are rigid. They do not depend on the order in terms of congruence (although the position of points may vary slightly depending on order, but the final figure is still a congruent image).
• Option 3: Since translation (4 units left, 1 unit down) and reflection (over the y - axis) are rigid transformations, the image (figure B) of figure A after these transformations is congruent to figure A.

Answer:

Figure B is the image of figure A after the transformations because the triangles are congruent.