Translations: description to algebraic rule | Grade 8 (TX) | Khan Academy

We're told Alicia translated quadrilateral PQRS four units to the left and three units up to create quadrilateral A' B' C' D'.

Write a rule to describe this transformation. So pause this video, have a go at it, and then we'll do it together.

All right, so when we talk about a rule to describe a transformation, we're talking about starting with (x, y) points that are, say, on the original shape PQRS, and then it's going to get mapped to new (x, y) coordinates.

And these, what the new x is, is going to be dependent on oftentimes the old x, or maybe some combination of the x's and the y's. Or in certain cases, it could even be the y.

But if we're just talking about a simple translation, it's going to be a shifting of this x, and if we talk, and it's going to be a shifting of this y for the new y-coordinate.

Now, on the x side, it says four units to the left. So whatever our x was before, we are now going to shift four to the left. The convention is we're going to subtract four if we're shifting four to the left.

And now, we're also going to shift three units up. So whatever the y-coordinate was before, we're now going three higher than that.

So it is y + 3, and we are done.