# 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 __________.