Question 1117805: find the image of the point under a dilation centered at (0,0) with the given scale factor simplify completely
(5/4,-3/2)
scale factor=1/10 equals (/,/)
Answer by greenestamps(13214)   (Show Source):
You can put this solution on YOUR website!
By definition, the image of a point (a,b) under a dilation centered at the origin (0,0) with scale factor n is the point (na,nb).
I think you should be able to figure out the answer.
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Let's look at the problem with numbers that are easier to work with.
In everyday usage, a dilation means something is getting bigger, as when the pupil of your eye gets larger when there is less light to allow you to see better.
As used in mathematics, a dilation can make things either bigger or smaller -- by whatever the scale factor is.
So a dilation with a scale factor of 3 makes thing 3 times as big; a dilation with a scale factor of 1/2 makes things half as big.
When the dilation is of a point with the dilation centered at (0,0), then the distance from (0,0) to the point is multiplied by the scale factor. Think of an arrow from (0,0) to the point; the dilation multiplies the length of the arrow by the scale factor, making it either longer or shorter.
For example, for a dilation of the point (3,5) with center at (0,0) and a scale factor of 4, the image of the point will be (3*4,5*4) = (12,20).
Or for a dilation of the point (-4,10) with center (0,0) and a scale factor of 1/2, the image of the point will be (-4/2,10/2) = (-2,5).
The numbers in your problem are just harder to work with, because the coordinates of the given point and the scale factor are all fractions.
The x coordinate of the image is the x coordinate of the given point, multiplied by the scale factor: (5/4) times (1/10).
The y coordinate is the y coordinate multiplied by the scale factor: (-3/2) times (1/10).
So finding the image is an exercise in multiplying and simplifying fractions....
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