Question

answer each question below.

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 7 units
○ translate figure a up 7 units
○ reflect figure a over the x-axis
○ reflect figure a over the y-axis
○ rotate figure a clockwise $180^{\circ}$ about the origin

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 5 units
○ translate figure c down 5 units
○ reflect figure c over the x-axis
○ reflect figure c over the y-axis
○ rotate figure c clockwise $90^{\circ}$ about the origin

Explanation:

For Figure A and B: Congruent figures have identical shape and size. Figure A and B match in dimensions. A 180° clockwise rotation about the origin maps A to B.
For Figure C and D: Figure C and D have identical shape and size, so they are congruent. Reflecting C over the x-axis flips it to match D's position.

Answer:

Left Section:

1. Are Figure A and Figure B congruent?

Yes

1. Which transformation will map Figure A onto Figure B exactly?

Rotate Figure A clockwise $180^\circ$ about the origin

Right Section:

1. Are Figure C and Figure D congruent?

Yes

1. Which transformation will map Figure C onto Figure D exactly?

Reflect Figure C over the x-axis