Question

(a) are figure a and figure b congruent?
o yes o no
(b) which sequence(s) of transformations will map figure a onto figure b exactly? choose all that apply.
o translate figure a to the left 10 units, and then reflect that result over the x - axis.
o reflect figure a over the y - axis, and then rotate that result counterclockwise 180° about the origin.
o reflect figure a over the y - axis, and then translate that result up 9 units.
o rotate figure a clockwise 90° about the origin, and then reflect that result over the x - axis.
o none of these

Explanation:

Step1: Check congruence definition

Two figures are congruent if they have the same shape and size. By observing the two figures, they have the same shape and size. So Figure A and Figure B are congruent.

Step2: Analyze transformation 1

For "Translate Figure A to the left 10 units, and then reflect that result over the x - axis": Translating Figure A 10 units left and reflecting over x - axis does not map it onto Figure B.

Step3: Analyze transformation 2

For "Reflect Figure A over the y - axis, and then rotate that result counter - clockwise 180° about the origin": Reflecting over y - axis and rotating 180° counter - clockwise about the origin maps Figure A onto Figure B.

Step4: Analyze transformation 3

For "Reflect Figure A over the y - axis, and then translate that result up 9 units": Reflecting over y - axis and translating up 9 units maps Figure A onto Figure B.

Step5: Analyze transformation 4

For "Rotate Figure A clockwise 90° about the origin, and then reflect that result over the x - axis": Rotating 90° clockwise about the origin and reflecting over x - axis does not map Figure A onto Figure B.

Answer:

(a) Yes
(b) Reflect Figure A over the y - axis, and then rotate that result counterclockwise 180° about the origin; Reflect Figure A over the y - axis, and then translate that result up 9 units