Distance and Midpoints

Lines and Line Segments
Can you measure the length of a LINE? Why?
Can you measure the length of a LINE SEGMENT?
Distance and Midpoints
[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]
Distance in the Coordinate Plane
[b]The Distance Formula:[/b] The distance between points (x[sub]1,[/sub]y[sub]1[/sub]) and (x[sub]2[/sub],y[sub]2[/sub]) is given by the formula [math]d=\sqrt{\left(x_2-x_1\right)^2+\left(y_2-x_2\right)^2}[/math] Note: This is really the Pythagorean Theorem in a different form.
[list=1][*]Plot the points (0,0) and (-4,3).[/*][*]Measure the distance between the two points.[/*][/list]
What distance did you get above? Find the distance by hand to check your answer from Geogebra.
Midpoints in the Coordinate Plane
To find the midpoint of a segment on a coordinate plane, find the average of your x and an average of your y values.[br][math]\left(x_m,y_m\right)=\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)[/math]
[list=1][*]Plot the points (-1,-3) and (3, 2).[/*][*]Connect the points with a segment and find the midpoint.[/*][/list]
What were the coordinates of the midpoint you calculated above?
Practice
[list=1][*]Plot two new points.[/*][*]Calculate the distance between the two points.[/*][*]Find the midpoint of the two points.[/*][/list]
Show the work to justify the answers Geogebra gave you on a piece of paper and then have Mr. Bosma check to see if yours are correct.
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Information: Distance and Midpoints