ACCESS - Dilation of Lines and Segments
- Author:
- Accesscd
- Topic:
- Dilation
Line AB is dilated with center of dilation at point C. Adjust the scale factor with the slider.
Adjust the scale factor to a value greater than 1.
1. What can you say about the position of line A'B' compared to line AB and point C? (Is it farther from point C than line AB, between line AB and point C, or on the other side of point C?)
2. Use A and B to adjust the slope of line AB. How does the slope of line A'B' change?
Adjust the scale factor to a value between 0 and 1.
3. What can you say about the position of line A'B' compared to line AB and point C?
4. Use A and B to adjust the slope of line AB. How does the slope of line A'B' change?
Adjust the scale factor to a value between 0 and -1.
5. What can you say about the position of line A'B' compared to line AB and point C?
6. Use A and B to adjust the slope of line AB. How does the slope of line A'B' change?
Adjust the scale factor to a value between less than -1.
7. What can you say about the position of line A'B' compared to line AB and point C?
8. Use A and B to adjust the slope of line AB. How does the slope of line A'B' change?
9. Adjust the scale factor to 0. What happens to line A'B'?
10. Adjust the scale factor to 1. What happens to line A'B'?
11. Adjust the scale factor to a number other than 1. Based on this and all of the experiments you did earlier, how can you describe the relationship between lines AB and A'B'? (Hint: look at their slopes.)
12. Move point A so that it is on C. This is now a line passing through the center of dilation. What happens to line A'B'? Check the scale factor to make sure this holds for all values.
Hide line AB and Show segment AB.
1. Change the scale factor for segment AB. What do you notice about the relationship of the ration A'B'/AB and the scale factor?
2. Complete the statements. Use the slider to test them if necessary.
a. If you dilate a segment AB to form a new segment A'B', the ratio ___/______ will be equal to the ______________.
b. If you dilate a segment AB to form a new segment A'B' by a scale factor greater than 1, segment A'B' will be ___________ than segment AB.
c. If you dilate a segment AB to form a new segment A'B' by a scale factor less than 1 but greater than zero, segment A'B' will be ___________ than segment AB.
d. If you dilate a segment AB by a scale factor of -1, the result would be the same as if you had ________________. (Hint - what other transformation would create this image?)