7.03 Transformations

Rigid transformations

There are three special kinds of transformations that we will quickly review.

Translations slide objects, without changing their orientation. The shape below has been translated by $5$5 units to the right and $5$5 units down:

Notice that each point is translated $5$5 units to the right and $5$5 units down along with it:

 

Reflections flip objects across a line:

Every point of the object is the same distance from the reflecting line, but on the opposite side:

The reflecting line may cross through an object, like this:

As before, each point on the original object is the same distance from the reflecting line, but on the opposite side. Points that lie on the reflecting line stay on the line:

An object that looks exactly the same before and after a reflection have an axis of symmetry. Here are some examples:

Rotations move an object around a central point by some angle. The shape below has been rotated $90^\circ$90°clockwise around the point $A$A.

 

We can imagine this rotation happening to every point in the shape. Importantly, each point will stay the same distance from the central point $A$A:

 

What makes these three kinds of transformations special is that the original shape and the transformed shape have the same properties:

• They have the same area
• Every side length stays the same
• Every internal angle stays the same

For this reason these three transformations are sometimes called rigid transformations. You can think of them as treating the shape as though it was made out of a rigid material, such as metal or hard plastic, with no stretching or squishing allowed.

 

 

Practice questions

Question 1

Question 2