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Dilating points

Dilate points on a grid and coordinate plane when given a scale factor.

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  • ohnoes default style avatar for user judahtodd
    What's the correct order? Do you across and then down or the opposite?
    (27 votes)
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    • piceratops ultimate style avatar for user watsonworms
      It actually doesn't matter! The key thing is that the dilation value affects the distance between two points. As in the first example (dilation by a factor of 3), A is originally 1 unit down from P and 2 units to the left of P.
      1*3 = 3, so A' (the dilated point) should be 3 units down from P.
      2*3 = 6, so A' should be 6 units to the left of P.

      It doesn't matter if you go left first or down first, because you always determine the location of A' with respect to P based on the location of A (which doesn't move) with respect to P.
      (2 votes)
  • hopper jumping style avatar for user Pei Lin
    What does that apostrophe at the end of "a"supposed to mean?
    (4 votes)
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  • piceratops ultimate style avatar for user alex
    How would you do it if there is no coordinate plane?
    (11 votes)
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    • male robot hal style avatar for user Commander Ben
      That's a great question!

      While a coordinate plane is helpful in making our measurements more exact and accurate, it is by no means necessary. In fact, in real world you wouldn't be using one.

      Let's imagine you are building a wall out of lego bricks that are all the same size. Each brick is 1 unit in length. When you line up 2 bricks end to end, that is dilation by a factor of 2! If you have four and you take one away, dilation by a factor of 3/4!

      This analogy can be extended to any number of real world objects, or even a line on a paper. Draw a line on a paper and measure it's length. Lay a ruler at one end and increase the line by two lengths, dilation by a factor of 3!

      I hope this answer was clear and understandable :)
      (21 votes)
  • blobby green style avatar for user Alijah Wali
    is this enlargement ? and what is a shear
    (10 votes)
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  • blobby green style avatar for user jp166787
    why would you go 6 down and 3 to the right? ()?
    (5 votes)
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  • marcimus orange style avatar for user Prarthana Sharma
    How do you determine the direction of the dilation?
    (5 votes)
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    • winston baby style avatar for user Tanner Henry
      If the point that you are dilating is directly above the point of dilation and you are dilating by 3, you take the distance from the point of dilation and the point you are dilating and you multiply it by 3. That is where you put your new point. If you draw a line from the point of dilation to the new point it should pass through the dilated point.

      Hope this helps. God bless!
      (4 votes)
  • piceratops seedling style avatar for user wright30
    SO I'm in 8th grade algerbra and um we're learning this at the begininng of the year and we have a test tomorrow and only talked about this for 3 days. I'm so confused when a problem just gives you the scale factor and doessn't give you an orgin. What do I do if the problem doesn't tell me the orgin but tells me the scale factor? How do I go about that?
    (5 votes)
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  • piceratops seedling style avatar for user adrian.galica
    Having some issues with determining whether you go down or across first in order to plot the dilation correctly. In a mastery question, Plot the image of point
    D under a dilation about point P with a scale factor of 1/3. since the graph does not have X,Y coordinates, P is in the top left of the graph and D is in the lower right. I went down then across in order to plot the dilation. This was wring because I was supposed to go across first, then down. How do I determine whether I go down or across first when calculating the dilation? thanks.
    (6 votes)
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  • female robot amelia style avatar for user Katherine Fuentes
    I'm confused, how does this work? If you dilate points you go how many ever points from the pre-image or the point of origin?

    Please help me because 2 hours of not understanding is killing my brain slowly!
    (5 votes)
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  • starky seedling style avatar for user alopez1543
    I don't understand this topic wth
    (4 votes)
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Video transcript

- [Instructor] We're asked to plot the image of point A under a dilation about point P with a scale factor of three. So what they're saying when they say under a dilation, they're saying stretching it or scaling it up or down around the point P. Now so what we're going to do is just think about, well how far is point A and then we want to dilate it with a scale factor of three. So however far A is from point P, it's going to be three times further under the dilation. Three times further in the same direction. So how do we think about that? Well, one way to think about it is to go from P to A you have to go one down and two to the left, so minus one and minus two. And so if you dilate it with a factor of three, then you're going to want to go three times as far down. So minus three, and three times as far to the left, so you'll go minus six. So one, let me do this, so negative one, negative two, negative three, negative four, negative five, negative six. So you will end up right over there. And you can even see it, that this is indeed three times as far from P in the same direction. So we could call the image of point A, maybe we call that A prime, and so there you have it. It has been dilated with a scale factor of three. And so you might be saying, wait, I'm used to dilating being stretching or scaling. How have I stretched or scaled something? Well imagine a bunch of points here that represents some type of picture and if you push them all three times further from point P, which you could do as your center of dilation, then you would expand the size of your picture by a scale factor of three. Let's do another example with a point. So, here we're told, plot the image of point A under a dilation about the origin with a scale factor of 1/3 so first of all we don't even see the point A here, so it's actually below the fold. So let's see, there we go, that's our point A. We want it to be about the origin, so about the point zero zero. This is what we want to, the dilation about the origin with a scale factor of 1/3, scale is 1/3. Scale factor, I should say. So how do we do this? Well here, however far A is from the origin we now want to be in the same direction, but 1/3 as far. So one way to think about it, to go from the origin to A you have to go six down and three to the right. So 1/3 of that would be two down and one to the right. Two is 1/3 of six and one is 1/3 of three, so you will end up right over here. That would be our A prime. So notice, you are 1/3 away from the origin as we were before because once again, this is point A under a dilation about the origin with a scale factor of 1/3.