Transcript 1-2 Measuring & Constructing Segments (continued)

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.
A
a
B
b
AB = |a – b| or |b - a|
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.
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 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
II
I
x-axis
III
IV
The location, or
coordinates, of a
point is given by an
ordered pair (x, y).
Midpoint Formula
The midpoint M of a AB with endpoints
A(x1, y1) and B(x2, y2) is found by
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.
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
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).