Line AB

Question

is on the coordinate plane and does not pass through the origin. Line AB
is dilated with a scale factor of 3 and a center of dilation at the origin to create line A′B′
. Describe the effects of the dilation on Line AB
. If line AB
was dilated with a scale factor of 13
, how would your answer change? 5 grade words

Answer 1

When we dilate line AB with a scale factor of 3 using the origin as the center of dilation, every point on line AB moves away from the origin to a new position that is three times as far from the origin. This means that if point A is at (x, y), after dilation, point A' will be at (3x, 3y).

The effects of the dilation are:

1. Lengthen: The distance between points A and B will increase because both points are moving farther from the origin.
2. Direction: The line will still be straight, and it will point in the same direction. The angles will stay the same.
3. Position: The line A'B' will lie in the same direction as line AB but will be stretched out.

If we dilate line AB with a scale factor of 13 instead, the same things happen, but even more so. Each point on line AB will move farther out — 13 times as far from the origin. So:

1. It will lengthen even more than the scale of 3.
2. The line will still be straight and point in the same direction.
3. The new line A''B'' will be stretched out much more than A'B'.

So, in both cases, the line gets longer and stays in the same direction, but the scale factor of 13 makes it much longer than with a scale of 3.