Translation

Hi, and welcome to this video on translation! Today, we’ll be looking at how this geometric transformation works and how we can successfully translate objects ourselves.

What is Translation

Translation is the sliding of an object such that its position changes but its size and shape are unchanged. It’s basically just moving a polygon around on a plane.

Translation Example

Let’s try translating a simple polygon, a quadrilateral, on the coordinate plane. Here’s our quadrilateral, which is a four-sided polygon.

We’re going to translate this polygon four units to the right and five units up. We’ll start by identifying the four vertices, or corners, of our polygon and labeling them A, B, C and D.

Once we have our points identified, we’re going to create a “prime” version of each one by adding 4 to our $x$-values and adding 5 to our $y$-values. In this case, we’re adding because we’re moving to the right and up, which is the positive direction for $x$– and $y$-values. If we were moving down or to the left we would need to subtract the amount of our translation from $x$ or $y$, respectively.

Okay, back to our points. Let’s start with point A, which is at $(-2,2)$. We take the $x$-value of point A and add 4 to it, giving us an $x$-value of positive 2 for A’. We take the y value of point A and add 5 to end up with 7. So, A’ is the point $(2,7)$. If we do the same thing to point B, we get $(6,10)$ for B’. Doing the same thing to C creates a C’ of $(10,7)$. Finally, we repeat the process one more time for point D and we end up with a D’ of $(6,4)$.

Now we can literally connect the dots to create our new, translated polygon.

Notice that our new polygon is the exact same size and shape as the old one. It’s just moved over four units and up five units. That’s all there is to it!

Practice Problems

Here are a few questions to test your knowledge before we go:

1. When translating a triangle left 3 units and up 2 units, where would point A’ be located if
point A is at (3,5)?

1. $(0,7)$
2. $(5,0)$
3. $(-5,2)$
4. $(0,-4)$

 
2. True or false: When translating a polygon, the “prime” points are all on the new, translated polygon.

 
3. True or false: When translating a polygon, the new, translated polygon will always be the same size and shape as the original.

 
That’s all for this review! Thanks for watching, and happy studying!

Geometric Transformation Practice Questions