Question

your answer is incorrect.
answer the questions about figure a and figure b below.
your answer
(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 down 9 units, and then reflect that result over the y - axis.
reflect figure a over the y - axis, and then translate that result down 9 units.
reflect figure a over the y - axis, and then rotate that result clockwise 180°
about the origin.
rotate figure a counterclockwise 180° about the origin, and then reflect that
result over the x - axis.
none of these

Explanation:

Step1: Check congruency

Congruent figures have the same shape and size. Since Figure A and Figure B have the same shape and size, they are congruent.

Step2: Analyze transformation sequences

• Option 1: Translating Figure A down 9 units changes its \(y -\)coordinate values. Then reflecting over the \(y -\)axis changes the \(x -\)coordinate sign. But this does not map Figure A to Figure B.
• Option 2: Reflecting Figure A over the \(y -\)axis changes the \(x -\)coordinate sign. Then translating down 9 units (subtracting 9 from \(y -\)coordinates) maps Figure A to Figure B.
• Option 3: Reflecting over the \(y -\)axis and then rotating \(180^{\circ}\) clockwise about the origin (which is equivalent to \((x,y)\to(-x, - y)\) after reflection \((x,y)\to(-x,y)\) and then rotation \((-x,y)\to(x, - y)\)) does not map Figure A to Figure B.
• Option 4: Rotating Figure A \(180^{\circ}\) counter - clockwise about the origin (\((x,y)\to(-x, - y)\)) and then reflecting over the \(x -\)axis (\((-x, - y)\to(-x,y)\)) does not map Figure A to Figure B.

Answer:

(a) Yes
(b) Reflect Figure A over the \(y -\)axis, and then translate that result down 9 units.