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 4 units
translate figure a up 4 units
reflect figure a over the x - axis
reflect figure a over the y - axis
rotate figure a clockwise 90° about the origin
rotate figure a counterclockwise 180° 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 180° about the origin
rotate figure c counterclockwise 90° about the origin
none of these

Explanation:

Step1: Check congruence of Figure A and Figure B

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

Step2: Determine transformation from Figure A to Figure B

The x - coordinates of corresponding points of Figure A and Figure B have opposite signs while y - coordinates remain the same. This is a reflection over the y - axis.

Step3: Check congruence of Figure C and Figure D

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

Step4: Determine transformation from Figure C to Figure D

The x - coordinates of corresponding points of Figure C and Figure D have opposite signs and y - coordinates have opposite signs. This is a rotation of 180° clockwise about the origin.

Answer:

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