Question

question 7 of 8 (1 point) | question attempt: 2 of unlimited
answer the questions about figure a and figure b below.
(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 5 units, and then reflect that result over the x - axis.
translate figure a down 6 units, and then rotate that result clockwise 180° about the origin.
reflect figure a over the x - axis, and then translate that result to the left 5 units.
rotate figure a counterclockwise 180° about the origin, and then reflect that result over the x - axis.
try again one of these

Explanation:

Step1: Check congruence

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 to the left 5 units and then reflecting over the x - axis.

Let's assume a general point \((x,y)\) on Figure A. After translation to the left 5 units, the point becomes \((x - 5,y)\). After reflection over the x - axis, the point becomes \((x - 5,-y)\). This sequence maps Figure A onto Figure B.

• Option 2: Translating Figure A down 6 units (point \((x,y)\to(x,y - 6)\)) and then rotating \(180^{\circ}\) clockwise about the origin (\((x,y)\to(-x,-y)\)) does not map Figure A onto Figure B.
• Option 3: Reflecting Figure A over the x - axis (\((x,y)\to(x,-y)\)) and then translating to the left 5 units (\((x,y)\to(x - 5,y)\)) maps Figure A onto Figure B.
• Option 4: Rotating Figure A counter - clockwise \(180^{\circ}\) about the origin (\((x,y)\to(-x,-y)\)) and then reflecting over the x - axis (\((x,y)\to(x,y)\)) (since reflection over x - axis of \((-x,-y)\) is \((-x,y)\)) does not map Figure A onto Figure B.

Answer:

(a) Yes
(b) Translate Figure A to the left 5 units, and then reflect that result over the x - axis; Reflect Figure A over the x - axis, and then translate that result to the left 5 units.