1. Lesson 1-3
Distance and Midpoint

2. 5-Minute Check on Lesson 1-2
Transparency 1-3
5-Minute Check on Lesson 1-2
Find the precision for a measurement of 42 cm.
If M is between L and N, LN = 3x – 1, LM = 4, and MN = x – 1, find x and MN?
Use the figure to find RT.
Use the figure to determine whether each pair of segments is congruent.
MN, QM
MQ, NQ
If AB  BC, AB = 3x – 2 and BC = 3x + 3, find x. R S T
2⅝ in
5¾ in M Q N
8 cm
6 cm
Standardized Test Practice: A 5 B 4 C 3 D 2
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3. 5-Minute Check on Lesson 1-2
Transparency 1-3
5-Minute Check on Lesson 1-2
Find the precision for a measurement of 42 cm.
If M is between L and N, LN = 3x – 1, LM = 4, and MN = x – 1, find x and MN?
Use the figure to find RT.
Use the figure to determine whether each pair of segments is congruent.
MN, QM
MQ, NQ
If AB  BC, AB = 4x – 2 and BC = 3x + 3, find x.
42 ± ½ cm or cm to 42.5 cm
x = 2, MN = 1 R S T
2⅝ in
5¾ in
8 ⅜ M Q N
8 cm
6 cm
8 = 8, Yes
8 ≠ 6, No
Standardized Test Practice: A 5 B 4 C 3 D 2
Click the mouse button or press the Space Bar to display the answers.

4. Objectives Find the distance between two points
Find the midpoint of a (line) segment

5. Vocabulary
Midpoint – the point halfway between the endpoints of a segment
Segment Bisector – any segment, line or plane that intersects the segment at its midpoint

6. Distance and Mid-points Review
Concept
Formula
Examples
Mid point
Nr line
Coord Plane
(a + b) 2
(2 + 8) 2
[x2+x1] , [y2+y1]
7 + 1 ,
Distance
D = | a – b |
D = | 2 – 8| = 6
D = (x2-x1)2 + (y2-y1)2
D = (7-1)2 + (4-2)2 = 40
= 5
= (4, 3)
(1,2)
(7,4) Y X ∆x ∆y D a b 1 2 3 4 5 6 7 8 9

7. Use the number line to find AX.
Answer: 8
Example 3-1b

8. Find the distance between E(–4, 1) and F(3, –1).
Method 1 Pythagorean Theorem
Use the gridlines to form a triangle so you can use the Pythagorean Theorem.
Simplify.
Take the square root of each side.
Example 3-2a

9. Method 2 Distance Formula
Simplify.
Simplify.
Answer: The distance from E to F is units. You can use a calculator to find that is approximately 7.28.
Example 3-2c

10. The coordinates of J and K are –12 and 16.
The coordinates on a number line of J and K are –12 and 16, respectively. Find the coordinate of the midpoint of . J K
-12 16
The coordinates of J and K are –12 and 16.
Let M be the midpoint of .
Simplify.
Answer: 2
Example 3-3a

11. Find the coordinates of M, the midpoint of
Find the coordinates of M, the midpoint of , for G(8, –6) and H(–14, 12).
Let G be and H be . y x
Answer: (–3, 3)
Example 3-3b

12. Let F be in the Midpoint Formula.
Find the coordinates of D if E(–6, 4) is the midpoint of and F has coordinates (–5, –3).
Let F be in the Midpoint Formula.
Write two equations to find the coordinates of D.
Example 3-4a

13. Answer: The coordinates of D are (–7, 11).
Solve each equation.
Multiply each side by 2.
Add 5 to each side.
Multiply each side by 2.
Add 3 to each side.
Answer: The coordinates of D are (–7, 11).
Example 3-4b

14. Summary & Homework Summary: Homework:
Distances can be determined on a number line or a coordinate plane by using the Distance Formula
The midpoint of a segment is the point halfway between the segment’s endpoints
Homework:
pg 25-27; 9, 12-15, 20, 23, 37-38, 57, 63, 65