Dilating Figures: Warmup Problem

1.  A line segment connects the points (1,1) and (5,8) on the grid below.  What are the coordinates of the midpoint of this line segment?  Explain how you found the midpoint and its coordinates.


[[{"fid":"164","view_mode":"default","type":"media","attributes":{"height":605,"width":622,"class":"media-element file-default"}}]]


2.  Below are a point C and a line segment [[{"fid":"166","view_mode":"default","type":"media","attributes":{"height":21,"width":27,"class":"media-element file-default"}}]].  The line segment is 8 cm long and has been divided into 8 equal parts.




Take a ruler and place one end on C, and measure the distance to one of the 8 marked points on [[{"fid":"168","view_mode":"default","type":"media","attributes":{"height":21,"width":27,"class":"media-element file-default"}}]].  Then double this distance and mark a new point at this new location.  We have done it for point B, in the picture below.  We measured and found the distance from C to B to be very close to 5 cm, so we doubled that to find point B’, a distance of 10 cm from C.

  [[{"fid":"339","view_mode":"full","type":"media","attributes":{"height":251,"width":251,"class":"media-element file-full"}}]]

Imagine that you have repeated the same process for the other 7 points on [[{"fid":"169","view_mode":"default","type":"media","attributes":{"height":21,"width":27,"class":"media-element file-default"}}]].   Predict what the new 8 points will look like.  Will they also be on a straight line?  How far apart will they be?  Now repeat the process we used to locate B’, for each of the 7 other points shown on [[{"fid":"169","view_mode":"default","type":"media","attributes":{"height":21,"width":27,"class":"media-element file-default"}}]].   Connect the 8 resulting points.  Do you get a new line segment?  How long is it?