Question

determining if figures are congruent and related by a transformation. 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 4 units. translate figure a down 4 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. 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 6 units. translate figure c up 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.

Explanation:

Step1: Analyze congruence of Figure A and B

Congruent figures have same shape and size. Figure A and B have different orientations and positions. By observing, they are mirror - images of each other across the y - axis. But their corresponding side - lengths and angles are equal, so they are congruent.

Step2: Determine transformation for Figure A to B

The transformation that maps Figure A onto Figure B exactly is a reflection over the y - axis. When a figure is reflected over the y - axis, the x - coordinates of its points change sign while the y - coordinates remain the same.

Step3: Analyze congruence of Figure C and D

Figure C and D have the same shape and size. They are in different positions. They are related by a translation. Since they have the same shape and size, they are congruent.

Step4: Determine transformation for Figure C to D

By observing the positions of Figure C and D, translating Figure C down 6 units will map it onto Figure D exactly.

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? Translate Figure C down 6 units