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 left 6 units
translate figure a down 6 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 right 8 units
translate figure c up 8 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 the same shape and size. By visual inspection, Figure A and Figure B have the same shape and size.

Step2: Determine transformation to map Figure A to Figure B

Translation is a slide. Moving Figure A to the left 6 units will map it onto Figure B.

Step3: Check congruence of Figure C and Figure D

By visual inspection, Figure C and Figure D have the same shape and size.

Step4: Determine transformation to map Figure C to Figure D

Reflection over the y - axis changes the sign of the x - coordinate. Reflecting Figure C over the y - axis will map it onto Figure D.

Answer:

For Figure A and Figure B:

• Congruence: Yes
• Transformation: Translate Figure A to the left 6 units

For Figure C and Figure D:

• Congruence: Yes
• Transformation: Reflect Figure C over the y - axis