Midpoint

Learning Outcomes :

 1. Identify the midpoint of a straight line joining two points.

 2. Find the coordinates of the midpoint of a straight line joining two points with :

                               I.            Common y-coordinates.

                               II.            Common x-coordinates.

 3. Find the coordinates of the midpoint of the line joining two points. 

 4. Pose and solve problem involving midpoints.

Identifying the Midpoints of Straight Lines

Activity

Aim            : To find the midpoint of a straight line

Instruction  : Carry out this activity in groups of four.

Materials   : Tracing paper, ruler and pencil.

Procedure :

1.      Draw a straight line on a piece of tracing paper, Label the line as PQ.

2.      Fold the tracing paper so that the two ends of the line overlap each other perfectly.

3.      Unfold the tracing paper, mark the folded part of the line as R.

4.      Is R equidistant from P and Q ? Discuss.

From the activity , we find that R is midpoint of the line PQ.




          Identify the midpoints of the following straight lines.

           a)

Points C is midpoint of AE.

b)                 

Points O is the midpoint of MQ.

The Midpoint of a Straight Line Joining Two Points with a Common y-     

coordinate

                     

In the above diagram, the point (0, 2) is the midpoint of the straight line joining 

points A(-2, 2) and B(2,2).

example:

Find the coordinates of the midpoint of a line joining points A(3, 6) and B(-7, 6).

answer:

The Midpoint of a Straight Line Joining Two Points with a Common x-

coordinate

In the diagram on the right, point (1, 0) is the midpoint of the straight line joining         

points A(1, 2) and B(1, -2).

                        

example:

Find the coordinates of the midpoint of the line joining points P(1, 0) and Q(1, - 4).

answer:

 x-coordinate for the midpoint = 1

Coordinates of the Midpoint of a Line Joining Two Points

example1:

               Find the coordinates of the midpoint of the line joining point M(-1, 5) to point                                            N(3,- 2).

answer:

example 2:

 Find the coordinates of the midpoint of the line joining F(8, 2) and G(0, -6).

answer: