When we dilate a line like line AB using a scale factor, we can think of it as enlarging or shrinking the line while keeping the same direction.
Dilation with a scale factor of 3:
- When line AB is dilated by a scale factor of 3 with the center of dilation at the origin, it means that every point on line AB is moved away from the origin to a new position that is 3 times farther away.
- This makes the new line, which we call line A′B′, longer than line AB. In other words, every point on line A′B′ is three times further from the origin than the corresponding point on line AB.
- Because we are dilating it around the origin, the line A′B′ will still be parallel to line AB, meaning they will never intersect, and they will have the same slope.
Dilation with a scale factor of 1/3:
- Now, if we dilate line AB with a scale factor of 1/3, it means that every point on line AB is moved closer to the origin to a new position that is 1/3 of the distance away.
- In this case, line A′B′ will be shorter than line AB. Every point on line A′B′ is one-third the distance from the origin compared to the corresponding point on line AB.
- Just like before, the line A′B′ will still be parallel to line AB and will have the same slope.
In summary:
- A dilation by a scale factor of 3 makes the line longer and moves points farther from the origin.
- A dilation by a scale factor of 1/3 makes the line shorter and moves points closer to the origin.
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