Google Classroom
GeoGebraGeoGebra Classroom

1 - 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

  1. Construct a line segment CD and find its length.
  2. 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 Toolbar Image that constructs midpoints and construct the midpoint of CD and label it E.
  3. 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.
  1. Plot the points (0,0) and (-4,3).
  2. 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.
  1. Plot the points (-1,-3) and (3, 2).
  2. Connect the points with a segment and find the midpoint.

Checkpoint

Show your teacher your work so far.

What were the coordinates of the midpoint you calculated above? Find the midpoint by hand and show your work using the fx menu.

Checkpoint

Show your teacher your work so far.

Practice

  1. Plot two new points.
  2. Calculate the distance between the two points.
  3. Find the midpoint of the two points.

Show the work to justify the answers Geogebra gave you below.

Final Checkpoint

Have your teacher check you work.