Dilating a Line: HSG.SRT.A.1.A
- 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 __________.