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

Lesson 2: Dilations

# Dilating points

Dilations are a way to stretch or shrink shapes around a point called the center of dilation. The amount we stretch or shrink is called the scale factor. If the scale factor is greater than 1, the shape stretches. If it's between 0 and 1, the shape shrinks.

## Want to join the conversation?

• What's the correct order? Do you across and then down or the opposite?
• 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.
• What does that apostrophe at the end of "a"supposed to mean?
• It is called "prime", it's there to say that the point is not the original point, but the image of the original one after transformation.

A = original point
A' = image of A

Hope that helps?
• How would you do it if there is no coordinate plane?
• 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 :)
• is this enlargement ? and what is a shear
• No, unless you’re dilating shapes by a factor that is greater than 1.
According to Wikipedia, a shear is “the component of stress coplanar with a material cross section.”

Hope that helps.
• 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?
• I think the origin is always the coordinate 0,0.
• How do you determine the direction of the dilation?
• 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!
• 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.
• why would you go 6 down and 3 to the right? ()?
• To get from the point of origin to A. Then divide those by 3 and you have A'. Do you think you can figure out where A' might be?

Hope this helps. God bless!
• 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?