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 up 8 units, and then reflect that result over the y - axis.
reflect figure a over the x - axis, and then translate that result to the right 7 units.
rotate figure a counterclockwise 180° about the origin, and then translate that result down 6 units.
rotate figure a counterclockwise 180° about the origin, and then reflect that result over the y - axis.
none of these

Explanation:

(a)

Step1: Congruent figures definition

Congruent figures have the same shape and size.

Step2: Analyze Figure A and B

By visual inspection, Figure A and Figure B have the same shape and size.

(b)

Step1: Check first transformation

Translate Figure A up 8 units (vertical movement), then reflect over \(y -\)axis (horizontal flip). This maps Figure A to Figure B.

Step2: Check second transformation

Reflect Figure A over \(x -\)axis (vertical flip) and translate right 7 units. This maps Figure A to Figure B.

Step3: Check third transformation

Rotate \(180^{\circ}\) (changes orientation) and translate down 6 units. Does not map correctly.

Step4: Check fourth transformation

Rotate \(180^{\circ}\) (changes orientation) and reflect over \(y -\)axis. Does not map correctly.

Answer:

(a) Yes
(b) Translate Figure A up 8 units, and then reflect that result over the \(y -\)axis; Reflect Figure A over the \(x -\)axis, and then translate that result to the right 7 units.