1A-4 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
Finding the Distance Formula
- 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 (x1,y1) and (x2,y2)? How could you find the distance between them?
What distance did you get above? Find the distance by hand to check your answer from Geogebra.
Midpoints in the Coordinate Plane
- 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 (x1,y1) and (x2,y2)
What were the coordinates of the midpoint you calculated above?