When we dilate line AB with a scale factor of 3 and the center of dilation at the origin, we are basically making the line longer and farther away from the origin.
For example, every point on line AB is moved away from the origin by a factor of 3. If a point on line AB is at coordinates (x, y), after the dilation, its new position (A′) will be at (3x, 3y). This makes the line A′B′ three times larger and keeps it parallel to the original line AB. Also, because the center of dilation is at the origin, line A′B′ will still not pass through the origin.
If we dilate line AB with a scale factor of 13 instead, the same thing happens, but each point on the line is moved even farther away from the origin. After dilation, a point that was at (x, y) becomes (13x, 13y). This means line A′B′ will be 13 times larger than the original line AB and still parallel to it.
In summary:
- With a scale factor of 3, the line is 3 times larger and still parallel, not going through the origin.
- With a scale factor of 13, the line is 13 times larger and still parallel, also not going through the origin. The larger the scale factor, the farther from the origin the new line will be!
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