Honors Geometry Section 1.2Measuring Lengths

Consider this number line.

On a number line, the real number assigned to a point is called the _________ of the point.

Find the distance between C and H.

coordinate

3

253

17

To find the distance between two points on a number line, take the absolute value of the difference

between the coordinates.For the previous problem.

3

25

3

12

3

13

3

12

3

13

The distance between the two points C and H is the same as the

length of , which can be writtenas ____ .

(Note: _________________).

CHCH

on topbar no

Consider this number line.

Examples: Find the distances.

AB = _______ GH = ________

HI = ________ GI = ________

3

21

3

21

1 3

22

While we are permitted to say AB = GH, we cannot say because they are not the exact same set of points. Instead we write

GHAB

GHAB

is congruent to

Postulate 1.2.2: If two segments have equal lengths, then they are

congruent.

“Tick” marks are used to indicate congruent segments in a figure.

A *midpoint of a segment is the point that divides the segment into

two congruent segments.

Example: On the number line at the top of the page, if I is the midpoint of , what is the coordinate of point J?

FJ

3

27

3

13

3

10FI

3

13IJ

3

27

3

13

3

14

On the number line at the top of the page, we determined that .

This illustrates the next postulate.

Postulate1.2.3: Segment Addition Postulate: If R is between P and Q, then ______________

Note: In order for one point to be between two other points, the points must be collinear.

3

22GIand,1,

3

21 HIGH

PQRQPR

Example: B is between A and C, AB = 13, BC = 5x and AC = 8x – 7. Determine x, BC and AC.

AB

C13

x5

78 x

78513 xx

3

20

320

7313

x

x

x

The Distance Formula and Midpoint FormulaFor any two points

AB =

the midpoint of AB =

),and),( 211 yB(xyxA 2

221

221 yyxx

2,

22121 yyxx

Example: If A(-3, 7) and B(9, -2), find AB and the midpoint of .AB

15225

81144

912

279-3-AB

22

22

AB

AB

AB

5.2,32

5,

2

6

2

27,

2

93

AB ofMidpoint