This lesson engages the students in discovering the formula for the midpoint of a line segment using graphs.
Students first graph some horizontal and vertical line segments locate the midpoint for those segments it is easily found when a line is horizontal or vertical. When two endpoints of a line segment are (-1,4) and (1, 4), the midpoint ends up being (0, 4). When two endpoints of a line segment are (-4, 6) and (-4, -6), the midpoint ends up being (-4, 0). Students are asked to explain how they determined the coordinates for the midpoints.
Then students are given several problems to find the midpoint for line segments that are not horizontal or vertical. By looking at the graph students often can figure out that the coordinates of the midpoint are the average of the two coordinates.
Five practice exercises are included. Graphing the information is encouraged by providing students coordinate grids with each exercise.
A full set of solutions is included.
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