Question

answer each question below.

left side:
figure a (a triangle) and figure b (a transformed triangle) on a coordinate grid.
question 1: are figure a and figure b congruent?
options: yes, no
question 2: which transformation will map figure a onto figure b exactly?
options: translate figure a to the left 5 units, translate figure a down 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

right side:
figure d (a triangle) and figure c (a transformed triangle) on a coordinate grid.
question 3: are figure c and figure d congruent?
options: yes, no
question 4: which transformation will map figure c onto figure d exactly?
options: translate figure c to the right 7 units, translate figure c up 7 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):

Are Figure A and Figure B congruent?

Congruent figures have the same shape and size. By observing Figure A and Figure B, we can see that they have the same shape and size (since one can be transformed into the other through a rigid transformation like rotation/reflection/translation). So the answer is Yes.

• Translating left/down: The orientation of Figure B relative to Figure A is not just a translation left or down.
• Reflecting over x - axis: Reflecting over x - axis would flip the figure vertically, but the orientation of Figure B doesn't match a simple x - axis reflection.
• Reflecting over y - axis: Reflecting over y - axis would flip the figure horizontally, which is not the case here.
• Rotating 90° clockwise: The rotation of 90° clockwise would change the shape's orientation in a way that doesn't match Figure B.
• Rotating 180° counter - clockwise: When we rotate Figure A 180° counter - clockwise about the origin, it will match the position and orientation of Figure B.
• None of these: Since rotating 180° counter - clockwise works, this is not correct.

Congruent figures have the same shape and size. By looking at Figure C and Figure D, we can see that they have the same shape and size (one can be transformed into the other through a rigid transformation like translation/rotation/reflection). So the answer is Yes.

Answer:

Yes

Which transformation will map Figure A onto Figure B exactly?