Question

is it possible to define a series of rigid transformations that takes figure a to figure b?
a yes, it can be defined with one reflection and one rotation
b yes, it can be defined with one rotation and one translation
c no, it cannot be defined because figure a and figure b are not congruent
d no, it cannot be defined because figure a and figure b are congruent.
consider two parallel lines separated by a distance of 10 units. if one line is translated 5 units to the right, will the lines remain parallel?
a yes, the lines will remain parallel.
b it depends on the y - intercepts of the lines.
c it depends on the slopes of the lines.
d no, the lines will not remain parallel.

Explanation:

Step1: Analyze the first question

• Rigid transformations (reflection, rotation, translation) preserve congruence.
• Figure A and Figure B are congruent.
• A rotation can change the orientation and a translation can move the figure to the position of the other figure.

Step2: Analyze the second question

• Translation is a rigid transformation.
• Parallel lines have the same slope.
• Translating a line (shifting it 5 units to the right) does not change its slope.

Answer:

1. B. Yes, it can be defined with one rotation and one translation
2. A. Yes, the lines will remain parallel