Geometry (all content)
Dilating shapes: expanding
Let's dilate a rectangle around a point P using a scale factor 1 2/3. This changes the size of the rectangle while keeping its shape. Because 1 2/3 is bigger than 1, most of the points get farther from P. Point P stays in place, because a distance of 0 times any scale factor is still 0. Created by Sal Khan.
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- I get almost all the video, but this one part confuses me. At1:19, where did Sal get the 3 to minus the 10 with?(48 votes)
- Point P is located at (-7,3) and the dilation needs to be 10 away from that. The 3 is the y-coordinate of the original point, so Sal subtracted the 10 from the positive 3 to get -7, the y-coordinate of the new point.(48 votes)
- How do you do a dilation when the scale factor is a percentage?(14 votes)
- you could make it into a decimal by dividing by 100 and then use that instead of the percentage. From that, it is basically the same as the video.
Hope it helps!(16 votes)
- What about dilating triangles?(14 votes)
- It's not hard. You just find the original line segment and then you multiply it by the scale factor. Just do that for all 3 sides. Then you get your new triangle!(6 votes)
- Is there a formula for this?(14 votes)
- if you're dilating about the origin then multiply all points' coordinates by however much you're dilating by yes?(0 votes)
- the problems on the practice are all triangles so this example that is being shown is not very helpful because triangles have a center that you have to account for and most of the triangles I had to do were off-centered/crooked which made it much harder..... just saying this video would be way more helpful if it included more shapes(10 votes)
- Rather than thinking of it as a triangle, think about having to move three points from the center. Each point has a horizontal and vertical distance from the dilation point, so whatever the scale factor is, multiply each part by the scale factor to find where the prime point should go. Do this three times, and you have the right answer. The prime points should be co-linear with their vertex point and the center of dilation. The shape does not matter as long as you do all the vertices the same way,(5 votes)
- Does anyone know a easier way to do this?(10 votes)
- Well, if you have a square, its very easy, just find the difference between the line segments, and because all the sides are the same so you just have to plot out the shape. But if you do this on a rectangle it's the same steps it just takes longer.(2 votes)
- At0:17, if the base shape is a triangle in which its sides and points are not on the marks of the graph, how do you expand the shape? Please help!(10 votes)
- So can I understand Dilation as this: The changing in the scale of a shape. ?(5 votes)
- Yeah, essentially. You increase or decrease the scale of a shape in a certain direction 👍(4 votes)
- When you reduce one, do you divide or multiply?(4 votes)
- ? If you mean reducing the side lengths of the shape by 1, you are dividing.(5 votes)
- Can u make the whole video more clear(6 votes)
The graph below contains the rectangle ABCP. Draw the image of ABCP under a dilation whose center is at P and a scale factor is 1 and 2/3. What are the lengths of the side AB and its image? So we're going to do a dilation centered at P. So if we're centering a dilation at P and its scale factor is 1 and 2/3, that means once we perform the dilation, every point is going to be 1 and 2/3 times as far away from P. Well P is 0 away from P, so its image is still going to be at P. So let's put that point right over there. Now point C is going to be 1 and 2/3 times as far as it is right now. So let's see, right now it is 6 away. It's at negative 3. And P, its x-coordinate is the same, but in the y direction, P is at 3. C is at negative 3. So it's 6 less. We want to be 1 and 2/3 times as far away. So what's 1 and 2/3 of 6? Well, 2/3 of 6 is 4, so it's going to be 6 plus 4. You're going to be 10 away. So 3 minus 10, that gets us to negative 7. So that gets us right over there. Now point A, right now it is 3 more in the horizontal direction than point P's x-coordinate. So we want to go 1 and 2/3 as far. So what is 1 and 2/3 times 3? Well that's going to be 3 plus 2/3 of 3, which is another 2. So that's going to be 5. So we're going to get right over there. Then we could complete the rectangle. And notice point B is now 1 and 2/3 times as far in the horizontal direction. It was 3 away in the horizontal direction, now it is 5 away from P's x-coordinate. And in the vertical direction, in the y direction, it was 6 below P's y-coordinate. Now it is 1 and 2/3 times as far. It is 10 below P's y-coordinate. So then let's answer these questions. The length of segment AB-- well, we already saw that. That is, we're going from 3 to negative 3. That is 6 units long. And its image, well it's 1 and 2/3 as long. We see it over here. We're going from 3 to negative 7. 3 minus negative 7 is 10. It is 10 units long. We got it right.