Defining translations
Narrator counts the directed segment as 6 units but then moves each vertex 5 units down, before noticing and correcting to 6 at about 80-102s. Interventions address the correction.
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The instructor translates kite ABCD by a directed line segment V that points straight down. The arrow's direction gives the direction of the move and its length gives the distance, so every vertex moves 6 units down. He first miscounts as 5, notices, and corrects every point to 6.
You'll be able to
- use a directed line segment to find the direction and distance of a translation.
- translate each vertex of a figure to plot its image.
- check my translation by confirming every point moved the same distance and direction.
Key words
- translation
- A slide that moves every point of a figure the same distance in the same direction.
- directed line segment
- A segment with an arrow; its direction and length tell you how a translation moves points.
- image
- The figure you get after a transformation.
- kite
- A four-sided shape with two pairs of equal adjacent sides.
Transcript
- [Instructor] Image of kite ABCD, which we see over here, under a translation by the directed line segment V, and we have this little tool here where we can put the image, or how we can plot it, so why don't you pause this video, have a go at this before we do it together?
Okay, now, let's do it together, so this directed line segment V right over here, it's clear that it wants us to make the image in the downward direction, essentially have a translation, that is a certain number of units down, and the length of this segment tells us that it needs to go one, two, three, four, five, six units down, so for example, the image of point B will be exactly five units below point B, one, two, three, four, five.
Image of point A, five units below A, one, two, three, four, five. Image of point D, five units below that. Whoops, this is having trouble. Lemme do C first. C, one, two, three, four, five, and then last but not least, point D, we go one, two, three, four, four, five.
Did I do that right? Actually, this actually looks like it's six. No, it's not going down by five, it's going down by six. Let me move all of these down by one more. I almost made a mistake, so let me see. Let go down by one more. Lemme make sure, so it's definitely, the arrow's going downwards, so we got that, and the length of this is one, two, three, four, five, six, and indeed, it looks like we've gone down six in every case, so it's looking good to me.
Yep, that's the image.
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