# Dilating a Line: HSG.SRT.A.1.A

- Author:
- Tim Brzezinski

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 __________.**