Line AB 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?(4 points
When line AB is dilated with a scale factor of 3 and a center of dilation at the origin to create line A'B', the effects of the dilation would be as follows:
1. The length of line AB would be multiplied by 3 to create line A'B'.
2. The direction of line AB would remain the same, but it would be stretched or compressed by a factor of 3.
3. The position of line AB may shift depending on its original position in relation to the origin.
If line AB was dilated with a scale factor of 13, the effects of the dilation would be similar to the previous scenario, but with a greater magnitude:
1. The length of line AB would be multiplied by 13 to create line A'B'.
2. The direction of line AB would remain the same, but it would be stretched or compressed by a factor of 13.
3. The position of line AB may shift more significantly compared to a dilation with a smaller scale factor.
In both cases, the line AB would be enlarged or reduced in size based on the scale factor of the dilation, while maintaining the same direction as the original line.
dumb it down
Sure! When you dilate a line with a scale factor of 3 and a center of dilation at the origin, the line will stretch or shrink by a factor of 3. This means that the line will become three times longer or three times shorter, but it will still point in the same direction. The line may also move a little bit depending on where it was originally.
If you dilate the line with a scale factor of 13 instead of 3, it will stretch or shrink by a factor of 13. This means it will become much longer or much shorter compared to dilating it with a scale factor of 3.
Overall, dilation with a larger scale factor will make the line change more dramatically in length compared to dilation with a smaller scale factor.