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?
The line moves closer to the center of dilation
4) What happens to the image of the line if k = 1?
The image lies on top of the pre image. It is congruent.
5) What happens to the image of the line if k = 0?
The image is on the center of dilation.
6) What happens to the image of the line if k < 0?
It passes the center of dilation. It reflected 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. Its transversal
Please answer the questions that appear below the applet as well !
Questions:
1) What happens if the original line m passes through point A?
They line on top of each other and they are congruent
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?
The pre 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 ___pre image_______.