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
- Construct a line segment CD 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 CD and label it E. - Measure the distances CE and ED. What do you notice about these two distances?
Distance in the Coordinate Plane
The Distance Formula: The distance between points (x1,y1) and (x2,y2) 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. Use the fx 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.
- 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? Find the midpoint by hand and show your work using the fx menu.
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 below.