Can you measure the length of a LINE? Why?
No, lines have infinite length. They never end.
Can you measure the length of a LINE SEGMENT?
Yes, because it has two endpoints you can measure the distance between those two points.
[list=1][*]Construct a line segment AB and find its length.[/*][*][b]Midpoint: [/b]the midpoint is the point equidistant from each endpoint. It is in the middle of the line segment. Find the tool in the point menu [icon]/images/ggb/toolbar/mode_point.png[/icon] that constructs midpoints and construct the midpoint of AB and label it C.[/*][*]Measure the distances AC and CB. What do you notice about these two distances?[br][/*][/list]
[b]Finding the Distance Formula[/b]
[list=1][*]Plot the points (1,-1) and (-2,3).[/*][*]Measure the distance between the two points.[/*][*]Where have you done this before?[/*][*]Move the line segment to a different location. How does that change the distance?[/*][*]What if you had any two points (x[sub]1[/sub],y[sub]1[/sub]) and (x[sub]2[/sub],y[sub]2[/sub])? How could you find the distance between them?[/*][/list]
What distance did you get above? Find the distance by hand to check your answer from Geogebra.
[math]\sqrt{\left(-2-1\right)^2+\left(3--1\right)^2}=\sqrt{9+16}=\sqrt{25}=5[/math]
[list=1][*]Plot the points (-1,-3) and (3, 2).[/*][*]Connect the points with a segment and find the midpoint.[/*][*]What if you had chosen different points? Move the points and find the new midpoint.[/*][*]How could you find the midpoint for any two given points (x[sub]1[/sub],y[sub]1[/sub]) and (x[sub]2[/sub],y[sub]2[/sub])[/*][/list]
What were the coordinates of the midpoint you calculated above?
(1,-0.5). [math]\left(\frac{-1+3}{2},\frac{-3+2}{2}\right)=\left(\frac{2}{2},\frac{-1}{2}\right)=\left(1,-0.5\right)[/math]