Video: Describing Translations of Points with Vectors

A translation of 3 units right and 2 units down can be described by the vector [3 and −2]. Describe the translation from point 𝐴 to point 𝐵 using a vector.

02:59

Video Transcript

A translation of three units right and two units down can be described by the vector three, negative two. Describe the translation from point 𝐴 to point 𝐵 using a vector.

So when we’re looking at translation, we’ve been told that we can express this using a vector. And to use a vector correctly, we have to look at the top and bottom part to see what it means. Well, we’re told that translation of three units right and two units down can be described by the vector three, negative two. So therefore, what we can do is identify that the top number is referring to the three units right and the bottom number is referring to the two units down.

So therefore, we can say that the top number refers to movement in the 𝑥-direction and the bottom number refers to movement in the 𝑦-direction. And we also know that if it’s negative, then it means it’s going left. And if it’s positive, then it’s going right. And we can tell that from what we’re told, because we were told that the translation is three units right. And the number in the vector was three or positive three.

So now let’s take a look at the bottom number. Well, for the bottom number, we can see that if it’s positive, it means that the translation is moving up. And if it’s negative, it’s moving down. And again, to confirm this, we can look back at the question, because we’re told that the translation has two units down. So therefore, when we look at the vector, we can see that it’s negative two. So that confirms that if it’s negative, it’s down, and if it’s positive, it’s up.

Okay, great. So now we know about the translations and the vectors to use to describe them. We can have a go and solve in the problem. And what we need to do is describe the translation from point 𝐴 to point 𝐵 using a vector.

So the first thing we’re gonna do is identify how far in the 𝑥-direction, so how far along, you would go to get from 𝐴 to 𝐵. And we can see that it’s five units right. And that’s because if we look at the scale, we go from negative two to three. And that’s five units.

Okay, great. So we now know the translation in the 𝑥-direction. Let’s have a look at it in the 𝑦-direction. Well, in the 𝑦-direction, we can see that we go three units up. That’s because we’re going from negative one to two. So this will be three units up.

So we now worked out what the translation is in words. Now we need to describe this using a vector. Well, the top number is going to be five. And that’s because it’s positive, because we’re going five units right. And the bottom number is also going to be positive. And it’s gonna be positive three. And that’s cause we’re moving three units up. So therefore, we can say for the translation from point 𝐴 to point 𝐵 described using a vector is five, three.

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