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

Vocabulary coordinate midpoint distance bisect length segment bisector congruent segments

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

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

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

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

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

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

It’s Mr. Jam-is-on Time!

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.

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.

1-6 Midpoint and Distance in the Coordinate Plane

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

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

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).

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

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

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

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)

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