6'7 Midpoint of a Line Segment

1
6.7 Midpoint of a Line Segment

• Meet Me Halfway

2
5-Minute Check on 6.6

• Find the slope-intercept form of the equation of
  a line through the point (4, -2) that is
• Parallel to the line 5x 3y 8
• Perpendicular to the line 5x 3y 8

3
6.7 Midpoint of a Line Segment

• With your partner, complete the Modeling
  Mathematics activity on page 370.
• Write a general rule for finding the midpoint of
  any segment.

4
Midpoint Formula

• The coordinates of the midpoint of a line segment
  whose coordinates are (x1, y1) and (x2, y2) are
  given by

5
In simple terms

• The midpoint is the average of the x- coordinates
  and the average of the y- coordinates.

6
Examples

• If the vertices of parallelogram ABCD are A(3,0),
  B(9,3), C(7,10), and D(1,7), prove that the
  diagonals bisect each other. That is, prove that
  they intersect at their midpoints.
• If P is the midpoint of line segment AB, find the
  coordinates of B given A(6,3) and P(1,5).

7
Zenos Paradox

• In the fifth century B.C., the Greek
  mathematician Zeno presented a version of this
  puzzle
• If a person is walking from Point A to Point B,
  the person must first walk half of the distance.
  Then the person must walk half of the remaining
  distance, then half of the remaining distance, so
  
• there will always be half the remaining distance
  to walk and the person will never reach Point B.
• Do you agree with Zenos reasoning? Why or why
  not?

8
Homework

• 6-6 25,27,33,34,50,53,54
• 6-7 3-11 odds, 40,46,48,51