6.7 Midpoint of a Line Segment Meet Me Halfway. 5-Minute Check on 6.6 n Find the slope-intercept form of the equation of a line through the point (4,

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6.7 Midpoint of a Line Segment Meet Me Halfway

5-Minute Check on 6.6 n Find the slope-intercept form of the equation of a line through the point (4, -2) that is 1. Parallel to the line 5x – 3y = 8 2. Perpendicular to the line 5x – 3y = 8

6.7 Midpoint of a Line Segment n With your partner, complete the Modeling Mathematics activity on page 370. n Write a general rule for finding the midpoint of any segment.

Midpoint Formula The coordinates of the midpoint of a line segment whose coordinates are (x 1, y 1 ) and (x 2, y 2 ) are given by

In simple terms: n The midpoint is the average of the x- coordinates and the average of the y- coordinates.

Examples n 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. n If P is the midpoint of line segment AB, find the coordinates of B given A(6,3) and P(1,5).

Zeno’s 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 Zeno’s reasoning? Why or why not?

Homework 6-6 #25,27,33,34,50,53, #3-11 odds, 40,46,48,51