When we have line AB on a coordinate plane and we dilate it with a scale factor of 3 from the origin, it basically means we are making the line longer and moving it away from the origin.
To understand this better, imagine you have a stretchy rubber band along the line AB. When you pull on the rubber band from the origin (like the center of a star), it stretches to 3 times its original distance from the origin. So, every point on line AB moves further away from the origin, and the new line we get is called line A'B'. This means both points A and B will be three times as far from the origin on the new line.
Now, if we change the scale factor to 13, the same thing happens, but it stretches the line even more. With a scale factor of 13, every point on line AB moves to a spot that is 13 times further from the origin. So, line A'B' from this dilation will be way longer than it was with the scale factor of 3. The line just gets further away from the origin, and it's also steeper or slanted in some way compared to how it originally was.
In summary, the bigger the scale factor, the more the line stretches away from the origin!