Question

transformations
determining if figures are congruent and related by a transformation
answer each question below.
(first image: coordinate plane with figure b (blue) and figure a (gray))
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 5 units
○ translate figure a up 5 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
(second image: coordinate plane with figure c (gray) and figure d (blue))
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 3 units
○ translate figure c down 3 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:

First Sub - Question (Figure A and Figure B)

1. Congruence Check: Congruent figures have the same shape and size. By visually inspecting Figure A and Figure B, we can see that they have the same shape and size, so they are congruent.
2. Transformation Check:

• Translating right or up will not map Figure A to Figure B as their orientations are mirrored.
• Reflecting over the x - axis will flip the figure vertically, not matching the mirroring over the y - axis.
• Reflecting Figure A over the y - axis (the vertical line \(x = 0\)) will map the points of Figure A to the corresponding points of Figure B. Rotating 90° or 180° will change the orientation in a way that does not match Figure B.

1. Congruence Check: Congruent figures have the same shape and size. By visually inspecting Figure C and Figure D, we can see that they have the same shape and size, so they are congruent.
2. Transformation Check:

• Translating left or down will not map Figure C to Figure D as their orientations are mirrored.
• Reflecting over the x - axis will flip the figure vertically, not matching the mirroring over the y - axis.
• Reflecting Figure C over the y - axis (the vertical line \(x=0\)) will map the points of Figure C to the corresponding points of Figure D. Rotating 180° or 90° will change the orientation in a way that does not match Figure D.

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

Second Sub - Question (Figure C and Figure D)