Translation:

 

a) This is a translation. As the squares move, the distances stay the same. If we named the top right corner on a square “point A” and named the bottom right corner “point B”, if you translated it to the right, you would get A’ and B’. Points A and A’ are the same distance apart as points B and B’.

b) As the squares move, the orientation also stays the same. If we named the top right corner on one of these squares “point A” it would become point A’ and point A” and even point A”‘ as it continues to be translated.

c) Special points are not possible for translations.

Rotation:

 

 

a) The distances are different. If a point on the tip of the star was A and a point towards the inside of the star was B then A and A’ wouldn’t have the same distances as B and B’

b) The orientation would be the same . The points if named in order either counterclockwise or clockwise will be in the exact same order after rotation.

c) The special point is the center of rotation

d) The center of rotation is the center of the star. I know this because if it were any other point, it wouldn’t rotate the same way.

e) The angle of rotation is 72 degrees. I know this because I divided 360 degrees by 5, which is the number of points on the star.

f) The order of rotation is order 5 because after rotating it each time, it would land on itself 5 times.

Reflection:

 

a) The distances are different because all the points (i.e. A and A’ and B and B’) would be different lengths apart from one another.

b) The orientation is different, in fact, it is reversed. If you went point A , point B, point C while reading it in a clockwise direction, it would go to point A’, point C’, point B’ when reading it in a clockwise direction.

c) The special points would be any points that lie on the body of the butterfly because that is where the line of reflection is.