In a rigid motion a figure is translated but its shape and size remains equal whereas in a dilation the size of the figure changes but its shape is conserved. Rigid motion transformations imply adding or substracting constant to the coordinates of the points belonging to a figure whereas in a dilation the x and y values are multiplied by the same number. This preserves the sahpe, if they are multiply by different numbers then it's no longer a dilation.
So let's analyze each transformation. The first one is:
[tex](x,y)\rightarrow(x-2,y-3)[/tex]As you can see you only substract constant from the original coordinates of each point which means that this transformation is a rigid motion.
The second transformation is:
[tex](x,y)\rightarrow(2x,3y)[/tex]Here both coordinates are multiplied by different numbers which means that this is neither a dilation or a rigid motion.
The third one is:
[tex](x,y)\rightarrow(3x,3y)[/tex]Both coordinates are multiplied by the same number which implies that this transformation is a dilation.
Finally the fourth one is:
[tex](x,y)\rightarrow(2-x,y)[/tex]Here the first coordinate is multiplied by -1 and the second remains the same so this is neither a dilation or a rigid motion.
Answersa. Rigid Motion
b. Neither
c. Dilation
d. Neither
