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
- Construct a line segment AB and find its length.
- Midpoint: 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 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?
Distance in the Coordinate Plane
The Distance Formula: The distance between points (x_{1,}y_{1}) and (x_{2},y_{2}) is given by the formula Note: This is really the Pythagorean Theorem in a different form.
- Plot the points (0,0) and (-4,3).
- Measure the distance between the two points.
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.
- Plot the points (-1,-3) and (3, 2).
- Connect the points with a segment and find the midpoint.
What were the coordinates of the midpoint you calculated above?
Practice
- Plot two new points.
- Calculate the distance between the two points.
- Find the midpoint of the two points.
Show the work to justify the answers Geogebra gave you on a piece of paper and then have your teacher check to see if yours are correct.