Question

are figure a and figure b congruent?
yes no
which transformation will map figure a onto figure b exactly?
translate figure a to the right 8 units
translate figure a up 8 units
reflect figure a over the x - axis
reflect figure a over the y - axis
rotate figure a clockwise 180° about the origin
rotate figure a counterclockwise 90° about the origin
none of these
are figure c and figure d congruent?
yes no
which transformation will map figure c onto figure d exactly?
translate figure c to the left 6 units
translate figure c down 6 units
reflect figure c over the x - axis
reflect figure c over the y - axis
rotate figure c clockwise 90° about the origin
rotate figure c counterclockwise 180° about the origin
none of these

Explanation:

Step1: Check congruence of Figure A and B

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

Step2: Determine transformation from A to B

By observing the position of vertices, rotating Figure A clock - wise 180° about the origin will map it onto Figure B.

Step3: Check congruence of Figure C and D

Figure C and D have same shape and size, so they are congruent.

Step4: Determine transformation from C to D

By observing the position of vertices, reflecting Figure C over the x - axis will map it onto Figure D.

Answer:

Are Figure A and Figure B congruent? Yes
Which transformation will map Figure A onto Figure B exactly? Rotate Figure A clockwise 180° about the origin
Are Figure C and Figure D congruent? Yes
Which transformation will map Figure C onto Figure D exactly? Reflect Figure C over the x - axis