Transcript Lesson 1 Contents - Headlee's Math Mansion

Lesson 1-3
Distance and Midpoint
Transparency 1-3
5-Minute Check on Lesson 1-2
1. Find the precision for a measurement of 42 cm.
2. If M is between L and N, LN = 3x – 1, LM = 4, and MN = x – 1,
find x and MN?
2⅝ in
3. Use the figure to find RT.
R
S
Use the figure to determine whether
each pair of segments is congruent.
8 cm
4. MN, QM
Q
If AB  BC, AB = 3x – 2 and
BC = 3x + 3, find x.
5
N
8 cm
Standardized Test Practice:
A
T
6 cm
M
5. MQ, NQ
6.
5¾ in
B
4
C
3
D
2
Click the mouse button or press the
Space Bar to display the answers.
Transparency 1-3
5-Minute Check on Lesson 1-2
1. Find the precision for a measurement of 42 cm.
42 ± ½ cm or
41.5 cm to 42.5 cm
2. If M is between L and N, LN = 3x – 1, LM = 4, and MN = x – 1,
find x and MN? x = 2, MN = 1
2⅝ in
8⅜
3. Use the figure to find RT.
R
S
Use the figure to determine whether
each pair of segments is congruent.
4. MN, QM
6.
8 cm
8 = 8, Yes
Standardized Test Practice:
5
B
4
N
8 cm
Q
If AB  BC, AB = 4x – 2 and
BC = 3x + 3, find x.
A
T
6 cm
M
8 ≠ 6, No
5. MQ, NQ
5¾ in
C
3
D
2
Click the mouse button or press the
Space Bar to display the answers.
Objectives
• Find the distance between two points
• Find the midpoint of a (line) segment
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
Distance and Mid-points Review
Concept
Mid point
Nr line
Formula
Examples
(a + b)
2
(2 + 8)
2
[x2+x1] , [y2+y1]
2
2
Coord Plane
Distance
Nr line
Coord Plane
D=|a–b|
(x2-x1)2 + (y2-y1)2
D=
=5
7 + 1 , 4 + 2 = (4, 3)
2
2
D = | 2 – 8| = 6
D = (7-1)2 + (4-2)2 = 40
Y
(7,4)
a
1
2
D
b
3
4
5
6
7
8
9
(1,2)
∆y
∆x
X
Use the number line to find AX.
Answer: 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.
Method 2 Distance Formula
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.
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
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)
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.
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).
Summary & Homework
• Summary:
– 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