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### Course: Geometry (all content)>Unit 10

Lesson 9: Old transformations videos

# Dilating lines

Sal shows how we can use dilations to map a line into another, parallel, line. Created by Sal Khan.

## Want to join the conversation?

• Why is this called a dilation and not a translation? I understand what it means to dilate a figure, to scale it up or down. But dilating a line seems to be simply a matter of changing its location; MOVING it up or down rather than SCALING it up or down.
• Technically, you can manipulate the scale factor and point of dilation to translate a line. This is pretty much all you can do by dilating a line, since a line, being infinite, stays infinite regardless of the scale factor.
• how to you find the scale factor
(1 vote)
• The scale factor is not always, given, in fact in most problems you must come up with a scale factor. First, think of two points. One point on the line that you are dilating, another point on the target for that point. Find the scale factor by dividing the distance to the target by the distance to the point on the line that you are dilating. Sorry if this was confusing, I'm not very good at explaining.
• how would we do this with shapes ?
• If you're using polygons with corners, just pick each vertex/corner and find its difference from the point of dilation. Since each edge of a shape is a line segment, just imagine you are dilating all the lines those segments lie on.
• If I am expected to find the scale factor for a dilation without being given numbers and only an image of a square within a square, how would that work?
• I'm really confused with how to do this.
• I watched the video several times and was still confused until speculating that a dilation might be like a shadow (projection). Unfortunately the problems don't have the scratchpad available, but if you could draw lines through corresponding original and image line segment endpoints, the intersection would provide a center of dilation. The scale is the ratio of the distances from the center to the corresponding endpoints.
• What if the scale factor is a fraction?
• what if your dilating by a fraction
• Can you use a negative number in your scale factor to make objects smaller? Or do you have to use fractions to make an object smaller?
• You use whole number to make it that much bigger. SF of 3 would make it 3 times bigger. In order to make a shape smaller you use fractions. A SF of 1/3 would make the shape 1/3 of its previous size.