UNIT 01 – LESSON 03 – DISTANCE & LENGTH Calculate with measures Find the distance between two points. Find the midpoint of a segment Locate a point on a segment given a

fractional distance from one endpoint.

RULER POSTULATE(CARD #8)

The points on a line can be matched one to one with the real numbers. The real number that corresponds to a point is the coordinate of the point.

The distance between points A and B, written as AB, is the absolute value of the difference of the coordinates of A and B.

BETWEENESSWhen three points are collinear, you can say that one point is between the other two.

If B is between A and C, then AB + BC = AC

If AB + BC = AC, then B is between A and C.

SEGMENT ADDITION POSTULATE(CARD #9)

Find the value of x and ST if T is between S and U, ST = 7x, SU = 45, and TU = 5x – 3.

CONGRUENT SEGMENTS Line segments that have the same

length are called congruent segments. You can say “the length of AB is equal to

the length of CD,” or you can say “AB is congruent to CD.”

The symbol ≅ means “is congruent to”

DISTANCE FORMULAIf A(x1, y1) and B(x2, y2) are points in a coordinate plane, then the distance between A and B is:

Find the distance between E(–4, 1) and F(3, –1).

Find the distance between A(–3, 4) and M(1, 2).

MIDPOINTSThe midpoint of a segment is the point that divides the segment into two congruent segments.

SEGMENT BISECTORSA segment bisector is a point, ray, line, or line segment, or plane that intersects the segment at its midpoint. A midpoint or segment bisector bisects a segment.

PARTITIONING A SEGMENT ON A NUMBER LINEFor a segment with endpoints at coordinates and , the point P with coordinate

partitions the segment in the ratio b:a.

MIDPOINT FORMULA ON A NUMBER LINEI has endpoints and on a number line, then the midpoint M of , has coordinate

DECORATING Marco places a couch so that its end is perpendicular and 2.5 feet away from the wall. The couch is 90” wide. How far is the midpoint of the couch back from the wall in feet?

MIDPOINT FORMULA ON A COORDINATE PLANEThe coordinates of the midpoint of a segment are the averages of the x-coordinates and of the y-coordinates of the endpoints.

If A(x1, y1) and B(x2, y2) are points in a coordinate plane, then the midpoint Mof has coordinates

M = ()

Find the coordinates of M, the midpoint of for G(8, -6) and H(-14, 12).

Find the coordinates of D if E(-6, 4) is the midpoint of and F has coordinates (-5, -3)

Find X on that is the distance from B to D.

Find P on that is of the distance from N to M.