Copy of Dilating a Line: HSG.SRT.A.1.A
In the applet below, line m is about to be dilated about point A. The scale factor of the dilation is given by the parameter k. (See below.)
1) Show the image of line m under a dilation about point A with scale factor k.
2) What does the image of this line look like? (Be specific!)
-It looks like a line.
3) Set the slider k = 5 to start. Then move the slider slowly to the left. Observe.
What happens to the image of m as k approaches zero?
- When moving the slider to the left the image moves closer to the image of dilation.
4) What happens to the image of the line if k = 1?
- When the image of line is at k=1 the image lies on top as the pre-image and it is congruent.
5) What happens to the image of the line if k = 0?
- When the image is at k=0 the image is on the center of dilation.
6) What happens to the image of the line if k < 0?
-When the image is k> 0 it reflects over the center of dilation.
Change the locations of point A and the original line m. Repeat steps 1-5 again.
6) Now, click the "Check This Out!" checkbox. Interact with the new slider you see.
Carefully observe what happens here.
- They are congruent because the lines are parallel.
Please answer the questions that appear below the applet as well !
Questions:
1) What happens if the original line m passes through point A?
More specifically, what does the image of m look like if m passes through A?
- If the original lines pass through point A they both line up because they are congruent.
2) What happens if the original line m does not pass through A?
What does the image of m look like if m does not pass through A?
- The image becomes parallel to the pre image.
3) Complete the following statement by filling in each blank with an appropriate word
to make a true statement:
A dilation maps a ___line____ not passing through the center of the
dilation to another ____line____ that is __parallel___ to the original
___pre image___. If, however, the original ___pre image__ passes through the
____center_____ of the dilation, the image of this line is the ___same___ as
the original _____line___.