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!)
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?
4) What happens to the image of the line if k = 1?
5) What happens to the image of the line if k = 0?
6) What happens to the image of the line if k < 0?
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.
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?
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?
3) Complete the following statement by filling in each blank with an appropriate word
to make a true statement:
A dilation maps a ___________ not passing through the center of the
dilation to another ___________ that is ________________ to the original
___________. If, however, the original ___________ passes through the
___________ of the dilation, the image of this line is the ____________ as
the original __________.