[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]2) What does the image of this line look like?  ([i]Be specific![/i])[br] - It looks like a line.  [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] -The image is moving closer to the center of dilation.  [br]4) What happens to the image of the line if k = 1?[br] - The image lays on top of the pre - image that is congruent. [br]5) What happens to the image of the line if k = 0?[br] - The image is on top of the center of dilation which makes it disappear. [br]6) What happens to the image of the line if k < 0?[br] - The image reflected over the center of dilation. [/color][br][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.  [br] - The transversal line makes the two angles congruent.[/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] - The pre -image and image lays on top of each other which makes them congruent. [br]2) What happens if the original line [i]m[/i] does [b]not[/b] pass through [i]A?  [br] - The image becomes parallel to the pre -image . [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][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 ____pre-image______.  [/b][/color]