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.
Use length and midpoint of a segment.
Apply distance and midpoint formula.
A point corresponds to one and only one number (or coordinate) on a number line.
AB = |a – b| or |b - a|
Distance (length): the absolute value of the difference of the coordinates.
Find each length.
BC = |1 – 3|
AC = |–2 – 3|
= |– 2|
= |– 5|
Point B is betweentwo points A and Cif and only if all three points are collinear and AB + BC = AC.
midpoint: the point that bisects, or divides, the segment into two congruent segments
4x + 15 = 7x
15 = 3x
5 = 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.
SV = 5x – 15. Find TS, SV, and TV.
GK = 24.Find x.
The location, or coordinates, of a point is given by an ordered pair (x, y).
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).
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
Use the Distance Formula to find the distance between A(1, 2) and B(7, 6).
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)
Use the Pythagorean Theorem to find the distance between J(2, 1) and K(7 ,7).