Definition: In Euclidean spaces: a set of points obtained by adding a given fixed vector to each point of a given set.
Alright class, settle down, let’s take a peek,
At the word ‘translate,’ a concept we seek!
The dictionary gives us a rather grand view,
Of Euclidean spaces, and what they can do.
“A set of points,” it states with such grace,
"By adding a vector to each one in its place!"
Let’s break that down, nice and slow, you see,
Think of a point – just simply
you
or
me
.
Now imagine a vector, a directional guide,
Like pushing forward, side to side, or wide!
You add that vector, shift it with care,
To every single point, everywhere there!
It's like moving shapes across the page,
A slide and a shuffle, a brand new stage.
Think of a drawing you want to relocate,
That’s translating – a simple little stroke!
So, 'translate' means to move something around,
Following a path, without a single sound.
Adding that vector - it's the key, don’t you see?
It changes the location for you and for me!
Do you have any questions about this shift? Let's discuss!