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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).