Question

When we dilate line AB with a scale factor of 3 and a center of dilation at the origin, every point on line AB moves away from the origin, getting 3 times farther from it. This means that the new line A′B′ will be parallel to line AB and will be three times as long. The distances between points on line A′B′ will be larger than those on line AB, but their shapes will stay the same, just like if we stretched a rubber band. If we instead dilate line AB with a scale factor of 13, the effect would be similar but even more pronounced. The line A′B′ in this case would be parallel to line AB and would stretch even further away from the origin, getting 13 times longer instead of just 3 times. So, even though both dilations change the size of the line and keep it parallel, the scale factor affects how far the new line moves from the origin and how much longer it becomes. Make this sound like a 7th grader

Answer 1

When we dilate line AB with a scale factor of 3 and center it at the origin, every point on line AB moves away from the origin and gets 3 times farther away. This means the new line, which we can call A′B′, is parallel to the original line AB but 3 times longer. The space between points on the new line A′B′ is bigger than on line AB, but the shapes stay the same, just like stretching a rubber band!

Now, if we dilate line AB with a scale factor of 13, it’s kind of the same idea but even more intense. The new line A′B′ will still be parallel to line AB, but it will stretch even more, becoming 13 times longer this time! So, both dilations keep the lines parallel and change their sizes, but the scale factor tells us how far away the new line moves from the origin and how much longer it gets.