1.3 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 CD 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 CD and label it E.[/*][*]Measure the distances CE and ED. 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. Use the f[sub]x[/sub] menu at the left to type in your work.

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? Find the midpoint by hand and show your work using the f[sub]x[/sub] menu.

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 below.