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### Course: Get ready for Precalculus > Unit 5

Lesson 2: Dilations# Dilating shapes: shrinking

Draw the image of the triangle under a dilation with scale factor 1/4 about the center of dilation on the coordinate plane.

## Want to join the conversation?

- Why do we need to know this(21 votes)
- You can use this knowledge for engineering. For example if you have a blueprint of a building which is dilated by a scale factor of 50, you can use that blueprint to actually build the house with perfect scaling. Also you can't forget exams.(7 votes)

- Somebody please help me! There is something I don't understand about dilation. which is what if the center if dilation is on of the points itself? And what if you count how many squares it is from the point of the origin what if the squares isn't complete? Like for example, the center of dilation is C and I count 4 up and 3 to the right, but one of the squares isn't entirely complete a part of it is out side the triangle. Also, the numbers that are at the triangles side (ex. ~5.8) do we multiply those by the scale factor? I hope that makes sense, please someone help...(9 votes)
- If the point of dilation is on a point, lets say "C," then when you dilated, the dilated C' would be on "C" and you would not even have to count squares of that one. It makes your life easier! :)(11 votes)

- Does someone mind explaining to me how to complete the practice? Its extremely confusing and nothing is helping. Thank you so much in advance. I understand the concept and everything, but when it comes to the practice, every question is marked incorrect. I've been stuck on dilations for quite some time now.(9 votes)
- I think I get what your saying, so if the dilation center was P and one point was 10 units away from P than you would only go 5 units away or as you said 1/2 of the distance from P to that point. When you do this for every single point you should construct larger or smaller dilated figure of the original one.(6 votes)

- how do you dilate shapes?(8 votes)
- you multiply the corresponding sides with the scale factor and create a new image, lemme know if it helped👍(6 votes)

- Why does sal have all the fancy number stuff on this screen? Why don't we have that!?(7 votes)
- it means
**approximately equal to**, and it would be kind of unnecessary for us to use it.(6 votes)

- what you do not understand ? be more specific(7 votes)

- Will the new line segments always be parallel to the original ones?(1 vote)
- Yes, as long as you don't rotate the shape, the corresponding sides will always be parallel.(2 votes)

- Why do
**dilating**shapes keep the same**angle**measure?(0 votes)- When you dilate the plane, you transform each point (x, y) into another point (rx, ry) for some scale factor r.

So say you have two points (a, b), (c, d). The slope of the line between them is (d-b)/(c-a).

After dilating, these points will be (ra, rb) and (rc, rd). The slope of the line between them will be

(rd-rb)/(rc-ra)=r(d-b)/r(c-a)=(d-b)/(c-a), exactly the same.

So a line after dilation will have the same slope as (be parallel to) the original line. So if two lines intersect at some angle, and we dilate the image, both lines will still be parallel to the originals, and so the angle is unchanged.(4 votes)

- I don't understand the concept of this(1 vote)
- You make each point [scale factor] * [distance between the dilation point and the other point.(1 vote)

## Video transcript

- [Instructor] We're told draw the image of triangle ABC under a dilation whose center is P and scale factor is 1/4. And what we see here is
the widget on Khan Academy where we can do that. So we have this figure, this triangle ABC, A, B, C, right over here, and what we wanna do is dilate it, so that means scaling it up or down, and the center of that
dilation is this point P. So one way to think
about it is let's think about the distance between point P and each of these points, and we wanna scale it by 1/4. So the distance is going to be 1/4 of what it was before. So, for example, this
point right over here, if we just even look
diagonally from P to A, we can see that we are
crossing one square, two squares, three squares, four squares. So if we have a scale factor of 1/4, instead of crossing
four squares diagonally, we would only cross one square diagonally. So I'll put the corresponding
point to A right over there. Now, what about for point C? It's not quite as obvious, but one way we could think about it is we can think about how
far are we going horizontally from P to C, and then how
far do we go vertically? So horizontally, we're going one, two, three, four, five, six,
seven, eight of these units, and then vertically we're
going one, two, three, four. So we're going to the
left eight and up four. Now, if we have a scale factor of 1/4, we just multiply each of those by 1/4. So instead of going to the left eight, we would go to the left two. Eight times 1/4 is two. Instead of going up
four, we would go up one. So this would be the
corresponding point to point C. And then we'll do the
same thing for point B. When we go from P to B,
we're going one, two, three, four, five, six, seven, eight up, and we're going four to the left. So if we have a scale factor of 1/4, instead of going eight
up, we'll go two up, and instead of going four to the left, we'll go one to the left. So there you have it. We have just dilated triangle ABC around point P with a scale factor of 1/4, and we are done.