Question

(a) are figure a and figure b congruent? yes no (b) which sequence(s) of transformations will map figure a onto figure b exactly? choose all that apply. translate figure a to the left 7 units, and then rotate that result counter - clockwise 90° about the origin. translate figure a down 9 units, and then reflect that result over the y - axis. reflect figure a over the y - axis, and then rotate that result clockwise 180° about the origin. rotate figure a counter - clockwise 180° about the origin, and then reflect that result over the x - axis. hints of steps try again

Explanation:

Step1: Recall congruence definition

Two figures are congruent if they have the same shape and size, which means one can be transformed into the other through translations, rotations, and reflections.

Step2: Analyze Figure A and B

By observing the two figures, we can see that they have the same shape and size. So the answer to (A) is yes.

Step3: Check transformation options for (B)

• Translating Figure A to the left 7 units and then rotating counter - clockwise 90° about the origin: Analyze the orientation and position changes. This sequence may not map Figure A onto Figure B exactly.
• Translating Figure A down 9 units and then reflecting over the y - axis: Analyze the orientation and position changes. This sequence may not map Figure A onto Figure B exactly.
• Reflecting Figure A over the x - axis and then rotating clockwise 180° about the origin: Analyze the orientation and position changes. This sequence may not map Figure A onto Figure B exactly.
• Rotating Figure A counter - clockwise 180° about the origin and then reflecting over the x - axis: Analyze the orientation and position changes. This sequence can map Figure A onto Figure B exactly.

Answer:

(A) yes
(B) Rotate Figure A counter - clockwise 180° about the origin, and then reflect that result over the x - axis.