Midpoint

1
Midpoint

• Of a line segment

2
What are co-ordinates?

• Co-ordinates are points on a plane, or graph.
  Here is an example of co-ordinates
• (5,7)
• This means, the point is 5 units to the right (on
  the horizontal x-axis) and 7 units up (on the
  vertical y-axis).
• Note that a co-ordinate must be written as two
  numbers inside a bracket, separated by a comma.

Y
7
X
5
3
What is a line segment?

• A line segment is a part of a line that lies
  between two points. Here is a line segment
• The co-ordinates of this line segment
  are (2,4) and (5,7).

Y
7
4
X
5
2
4
So, what is a midpoint?

• A midpoint of a line segment is the co-ordinates
  of the point that lies exactly halfway between
  the two points. So, the co-ordinates of the
  example line segments midpoint is (3.5,5.5).

Y
7
5.5
4
X
5
2
3.5
5
How do we figure out the midpoint?

• To work out the midpoint, first add together both
  the x points and divide the answer by two. This
  gives you the x value of the midpoint.
• Then, repeat this with the y values to get the y
  value of the midpoint.
• Write these two values as a co-ordinate, and you
  have the midpoint!

6
An example

• This is how to figure out the midpoint of the
  example line segment.
• The x values are 2 and 5.
• Add them together to get7. Divide this by two,
  andyou get 3.5.
• The y values are 4 and 7. Adding them gets11.
  Half of this is 5.5.
• So, the midpoint is at (3.5 , 5.5)!

Y
X
5
2
3.5
Y
7
5.5
4
X
5
2
3.5
7
Exercise and Homework

• The exercise, 16.1, is on page 127.
• Your assigned homework is 18.01 on page 77.
  (There is only 4 questions! ?)