1. 1-2 Measuring Segments Objectives
Use length and midpoint of a segment.
Apply distance and midpoint formula.

2. Vocabulary coordinate midpoint distance bisect
length segment bisector congruent segments

3. A point corresponds to one and only one number (or coordinate) on a number line.

4. Distance (length): the absolute value of the difference of the coordinates.
AB = |a – b| or |b - a| A a B b

5. Example 1: Finding the Length of a Segment
Find each length.
A. BC
B. AC
BC = |1 – 3|
AC = |–2 – 3|
= |– 2|
= |– 5|
= 2
= 5

6. Point B is between two points A and C if and only if all three points are collinear and AB + BC = AC. A

9. bisect: cut in half; divide into 2 congruent parts
bisect: cut in half; divide into 2 congruent parts. midpoint: the point that bisects, or divides, the segment into two congruent segments

10. 4x + 6 = 7x - 9
4x + 15 = 7x
-4x x
15 = 3x 3
5 = x

11. It’s Mr. Jam-is-on Time!

12. Recap! 1. M is between N and O. MO = 15, and MN = 7.6. Find NO.
2. S is the midpoint of TV, TS = 4x – 7, and SV = 5x – 15. Find TS, SV, and TV.
3. LH bisects GK at M. GM = 2x + 6, and
GK = 24. Find x.

13. 1. M is between N and O. MO = 15, and MN = 7.6. Find NO.

14. 2. S is the midpoint of TV, TS = 4x – 7, and
SV = 5x – 15. Find TS, SV, and TV.

15. 3. LH bisects GK at M. GM = 2x + 6, and
GK = 24. Find x.

16. 1-6 Midpoint and Distance in the Coordinate Plane

17. Vocabulary
Coordinate plane: a plane that is divided into four regions by a horizontal line called the x-axis and a vertical line called the y-axis.
y-axis
The location, or coordinates, of a point is given by an ordered pair (x, y). II I
x-axis
III IV

18. Midpoint Formula The midpoint M of a AB with endpoints
A(x1, y1) and B(x2, y2) is found by

19. Find the midpoint of GH with endpoints G(1, 2) and H(7, 6).
Example
Find the midpoint of GH with endpoints G(1, 2) and H(7, 6).

20. Example M(3, -1) is the midpoint of CD and C has coordinates (1, 4).
Find the coordinates of D.

21. The distance d between points A(x1, y1) and B(x2, y2) is
Distance Formula
The distance d between points A(x1, y1) and B(x2, y2) is

22. Example
Use the Distance Formula to find the distance between A(1, 2) and B(7, 6).

23. Pythagorean Theorem a2 + b2 = c2
In a right triangle,
a2 + b2 = c2
c is the hypotenuse (longest side, opposite the right angle)
a and b are the legs (shorter sides that form the right angle)

24. Example
Use the Pythagorean Theorem to find the distance between J(2, 1) and K(7 ,7).