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The point halfway between the endpoints of a given segment is called the midpoint.

The point halfway between the endpoints of a given segment is called the midpoint. Midpoint between two points :.

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The point halfway between the endpoints of a given segment is called the midpoint.

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  1. The point halfway between the endpoints of a given segment is called the midpoint. Midpoint between two points : Today we will explore the Essential Question, “What is the method for finding the midpoint between two given points on a coordinate plane?” A midpoint divides a line segment into two equal parts. To find the midpoint of a line segment on a coordinate plane, find the average of the x-coordinates and the average of the y-coordinates. These averages will be the x and y coordinates of the midpoint of the given segment. The concept of finding these averages can be written as a formula and it is written on the FCAT Mathematics Reference Sheet as shown in the box.

  2. Example 1: Find the midpoint of a segment with endpoints at and . Name the coordinates of and the coordinates of as as and substitute into the formula as follows: Therefore, the midpoint of the segment is (1,5).

  3. y Point X is located at and point Y is located at . Name the coordinates of as x and the coordinates of as Therefore, point Z is located at . 10 8 6 X 4 2 -10 -8 -6 -4 -2 0 2 4 6 8 10 -2 -4 Y -6 -8 -10 Example 2: Point Z is the midpoint of a segment with endpoints at X and Y with integer coordinates as shown in the diagram. Find the coordinates of point Z. It is necessary to first find the coordinates of points X and Y. . and substitute into the formula as follows:

  4. y x 10 W 8 4 Y 2 Z -10 -8 -6 -4 -2 0 2 4 6 8 10 -2 X -4 6 -6 -8 -10 • Guided Practice Problems: • Find the coordinates of the midpoint of a segment with endpoints at W and Y. (2, 9) Y is located at (8, 3). W is located at (2, 9). (8, 3) (3, 1) Name (2, 9) as and (8, 3) as . (-3,-3) • Find the coordinates of the midpoint of a segment with endpoints at X and Y. 3. Find the coordinates of the midpoint of a segment with endpoints at W and Z. X is located at (-3, -3). Y is located at (8, 3). Name (-3, -3) as and (8, 3) as . W is (2, 9). Z is (3, 1).

  5. 4. If the coordinates of the endpoints of a segment are located at , find the coordinates of the midpoint. Name the coordinates of and the coordinates of as as and substitute into the formula as follows: Therefore, the midpoint of the segment is . NOTE: The fraction can be written as 2.5.

  6. y • If the coordinates of the endpoints of a segment are located at • , find the coordinates of the midpoint. Name the coordinates of and as as . x 10 8 6 4 2 -10 -8 -6 -4 -2 0 2 4 6 8 10 -2 -4 -6 -8 -10 Independent Practice: 2. A monorail at an amusement park has stops at points W and Z as shown on the coordinate plane. A new stop needs to be inserted at the midpoint of the segment with endpoints at W and Z. What are the coordinates of the location of the new stop? W Z is located at (10, -9). W is located at (-6, 6). Name (-6, 6) as and (10, -9) as . Z

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