Translations: description to algebraic rule
About this video
Quadrilateral PQRS is translated 4 units left and 3 units up. The video explains that a translation rule shifts x and y separately, giving (x, y) -> (x - 4, y + 3).
You'll be able to
- turn a written description of a translation into an algebraic rule.
- decide whether to add or subtract for left, right, up and down.
Key words
- translation
- A slide of a shape where every point moves the same distance in the same direction.
- rule
- A description like (x, y) -> (x - 4, y + 3) that tells where each point is mapped.
- coordinates
- The pair (x, y) that gives a point's position on a grid.
Transcript
- [Instructor] We're told Alicia translated quadrilateral P-Q-R-S four units to the left and three units up to create quadrilateral A prime, B prime, C prime, D prime. Write a rule to describe this transformation. So pause this video, have a go at it and then we'll do it together.
Alright, 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, P-Q-R-S, and then it's going to get mapped to new X and 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 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. To the left, the convention is we're going to subtract four which we'll be shifting four to the left and now we're also gonna shift three units up.
So whatever the Y coordinate was before, we're now going three higher than that. So it is Y plus three and we are done.
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