[color=#000000]In the applet below, line [i]m[/i] is about to be dilated about point [i]A.  [/i]The [i]scale factor[/i] of the dilation is given by the parameter [i]k[/i].  (See below.)  [i] [/i][/color][br][br][color=#980000]1) Show the image of line m under a dilation about point [i]A[/i] with scale factor k.  [br] It looks like a line[br]2) What does the image of this line look like?  ([i]Be specific![/i])  [br] Its a straight line that is in an angle[br]3) Set the slider k = 5 to start.  Then move the slider slowly to the left.  Observe.[br]    What happens to the image of m as k approaches zero?  [br] [i]The image moves closer to the center of dilation[/i][br]4) What happens to the image of the line if k = 1?[br] Image and pre-image become congruent[br]5) What happens to the image of the line if k = 0?[br] The image is on the center of dilation[br]6) What happens to the image of the line if k < 0?[/color][br] The image reflectes over the center of dilation[br]Change the locations of point [i]A[/i] and the original line [i]m[/i].  Repeat steps 1-5 again.  [br][br][color=#980000]6) Now, click the "Check This Out!" checkbox.  Interact with the new slider you see.  [br]    Carefully observe what happens here.  [/color][br][br][i][color=#1e84cc][b]Please answer the questions that appear below the applet as well !  [/b][/color][/i]

[b][color=#980000]Questions:  [/color][br][br][/b][color=#000000]1) What happens if the original line [i]m[/i] passes through point [i]A[/i]?  [br]    More specifically, what does the image of [i]m[/i] look like if [i]m[/i] passes through [i]A[/i]?  [br] They line up together and are also congruent[br]2) What happens if the original line [i]m[/i] does [b]not[/b] pass through [i]A?  [br][/i]    What does the image of [i]m[/i] look like if [i]m[/i] does [b]not[/b] pass through [i]A[/i]?  [br] The image becomes parallel to the pre-image [br]3) Complete the following statement by filling in each blank with an appropriate word[br]    to make a true statement:  [/color][br][br]    [color=#0000ff][b]A dilation maps a _____line______ not passing through the center of the[br][br][/b]    [b]dilation to another _____line______ that is ________parallel________ to the original[br][br][/b]    [b]_____pre-image______.  If, however, the original ______pre-image_____ passes through the [br][br][/b]   [b]______center_____ of the dilation, the image of this line is the _____same_______ as[br][br][/b]   [b]the original ____line______.  [/b][/color]