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Translations: graph to algebraic rule | Transformational geometry | Grade 8 (TX) | Khan Academy

2m read
·Nov 10, 2024

We are told Lucas translated triangle ABC to create triangle A'B'C'. So we went from this blue one, or blue-green one, to this burgundy one, or this red one. Write a rule that describes this transformation. So pause this video and try to figure this out on your own before we do this together.

All right, so when we look at what's going on here, actually they tell us what type of transformation it is. This is a translation, and we could tell it hasn't been dilated, that the triangles look like they're the same size. For example, if we go from A' to B', it's down 2 and to the right 1. And if we look at going from A to B, it's also down 2 and to the right 1. So they're the same size; they haven't been scaled, but they definitely have been translated.

Triangle ABC has been translated to get us to A'B'C'. To think about what that translation is, we just have to say, "Okay, for each of these points, what happened to them? How did they get moved?" Well, it looks like for example Point C right over here, to go from C to C', we had to go, it looks like, how many units down is that? One, two, three, four, five. So we had to go five units down, and then we had to go, it looks like, one, two, three, four, five, six units to the left.

Just based off of that, it looks like the other ones have done the same, but I can double-check that. The rule I would say is for every x and y for A, B, and C, we have now mapped it where in the x-direction we have been shifted to the left by six. So whatever our original x was, we are now going to subtract by six. Whatever our original y was, we are now going to be five lower, so we're going to subtract by five.

So that's the rule, and we could double-check it with one of these other points. For example, we could look at, let's say Point B. If we go down five, we will end up right over here. Then, if we go to the left six, we are going to end up right over there at B'. So this rule definitely describes this translation.

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