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 and it is parallel
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?
It translates closer to the center of dilation
4) What happens to the image of the line if k = 1?
It lies directly on the pre-image and is also congruent
5) What happens to the image of the line if k = 0?
It lies directly on the center of dilation
6) What happens to the image of the line if 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.
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?
they lay right on top of eachother and 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?
They stay parallel
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 congruent to the original
line. If, however, the original line passes through the
center of the dilation, the image of this line is the congruent as
the original line.