1-2 measuring segments use length and midpoint of a segment. apply distance and midpoint formula....

1-2 Measuring Segments

Use length and midpoint of a segment.

Apply distance and midpoint formula.

Objectives

coordinate midpointdistance bisectlength segment bisector

congruent segments

Vocabulary

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

AB = |a – b| or |b - a|A

a

B

b

Distance (length): the absolute value of the difference of the coordinates.

Example 1: Finding the Length of a Segment

Find each length.

= 2

A. BC B. AC

= |– 2|

BC = |1 – 3|

= 5= |– 5|

AC = |–2 – 3|

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.

midpoint: the point that bisects, or divides, the segment into two congruent segments

4x + 6 = 7x - 9

+9 +94x + 15 = 7x-4x -4x

15 = 3x3 35 = 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

x-axis

I

III

II

IV

The location, or coordinates, of a

point is given by an ordered pair (x, y).

Midpoint FormulaThe midpoint M of a AB with endpoints

A(x1, y1) and B(x2, y2) is found by

ExampleFind the midpoint of GH with endpoints

G(1, 2) and H(7, 6).

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

Distance FormulaThe distance d between points A(x1, y1) and B(x2, y2) is

ExampleUse the Distance Formula to find the distance

between A(1, 2) and B(7, 6).

Pythagorean TheoremIn a right triangle,

a2 + b2 = c2

a and b are the legs (shorter sides that form the right angle)

c is the hypotenuse (longest side, opposite the right angle)

ExampleUse the Pythagorean Theorem to find the

distance between J(2, 1) and K(7 ,7).