Prentice Hall Lesson 11.3
EQ: What is the distance formula?
Midpoint
formula?
BOP: A radioactive isotope decays
exponentially. If the isotope has a half-life of 9
years and 0.696 mg remains after 36 years,
what was the size of the initial sample?
ALGEBRA 1 LESSON 11-2
pages 587–590 Exercises
2. 25
24. no
4. 26
26. 1.5
6. 1
28. 3
8. 5
30. 2.6
10. 7.1
12. 0.6
32. a. 6 5 ft
b. 80.5 ft2
14. about 15.5 ft
34. no
16. yes
18. no
20. no
22. yes
11-2
ALGEBRA 1 LESSON 11-2
36. yes
38. 1000 lb
40. 9.0
42. a. These lengths could be
2 legs or one leg and
the hypotenuse.
b.about 12.8 in. or 6 in.
44. a. 6.9 ft
b.89.2 ft2
c. 981 watts
46. a. Answers may vary.
Sample: 5, 20, 5
b.5 units2
48. An integer has 2 as a factor;
the integer is even; if an
integer is even, then it has 2
as a factor; true.
11-2
ALGEBRA 1 LESSON 11-2
50. You are in Brazil; you are
south of the equator; if you
are south of the equator you
are in Brazil; false.
52. 52 units2
54. 10
56. 5
11-2
Prentice Hall Lesson 11.3
EQ: What is the distance formula?
Midpoint
formula?
Toolbox:
• The Distance Formula: The distance “d”
between any two points (x1, y1) and (x2, y2) is
d = √(x2 – x1)² + (y2 – y1)²
• The Midpoint Formula: The midpoint of a
line segment with endpoints A(x1, y1) and
B(x2, y2) is: (x1 + x2 , y1 + y2)
2
2
ALGEBRA 1 LESSON 11-3
Find the distance between F(6, –9) and G(9, –4).
d=
( x2 – x1)2 + (y2 – y1)2 Use the distance formula.
d=
(9 – 6)2 + [–4 – (–9)]2 Substitute (9, –4) for (x2, y2)
and (6, –9) for (x1, y1).
d=
9 + 25
Simplify within parentheses.
d=
34
Simplify to find the exact
distance.
d
5.8
Use a calculator. Round to
the nearest tenth.
The distance between F and G is about 5.8 units.
11-3
ALGEBRA 1 LESSON 11-3
Find the exact lengths of each side of quadrilateral EFGH. Then find
the perimeter to the nearest tenth.
The perimeter =
EF =
=
=
=
[4 – (–1)]2 + (3 - 5)2
52 + (–2)2
25 + 4
29
FG =
=
=
=
(3 – 4)2 + (–2 – 3)2
(–1)2 + (–5)2
1 + 25
26
GH =
|–2 – 3| = 5
EH =
=
=
=
[–2 – (–1)]2 + (–2 – 5)2
(–1)2 + (–7)2
1 + 49
50
29 +
26 + 5 +
50
11-3
22.6 units.
ALGEBRA 1 LESSON 11-3
Find the midpoint of CD.
x1+ x2 y1+ y2
2 ,
2
(–3) + 5 7 + 2
=
, 2
2
2 9
= 2,2
Substitute (–3, 7) for
(x1, y1) and (5, 2) for
(x2, y2).
Simplify each numerator.
1
Write 9 as a mixed
= 1, 42
2
number.
1
The midpoint of CD is M 1, 4 2 .
11-3
ALGEBRA 1 LESSON 11-3
A circle is drawn on a coordinate plane. The endpoints of the diameter
are (–3, 5) and (4, –3). What are the coordinates of the center of the
circle?
x1+ x2 y1+ y2
2 ,
2
=
(–3) + 4 5 + (–3)
,
2
2
1 2
= 2,2
1
= 2, 1
1
The center of the circle is at 2 , 1 .
11-3
Substitute (–3, 5) for
(x1, y1) and (4, –3) for
(x2, y2).
ALGEBRA 1 LESSON 11-3
1. Find the distance between M(2, –1) and N(–4, 3) to the nearest
tenth.
7.2
2. Find the distance between P(–2.5, 3.5) and R(–7.5, 8.5) to the
nearest tenth. 7.1
3. Find the midpoint of AB, A(3, 6) and B(0, 2).
(11 , 4)
2
4. Find the midpoint of CD, C(6, –4) and
D(12, –2).
(9, – 3)
5. Find the perimeter of triangle RST to the
nearest tenth of a unit.
9.5 units
11-3
8th grade EOG Review:
• Clear desk except for work paper, pencil,
BLUE calculator.
• DO NOT WRITE ON THE TEST PAPER!!!
• Record your answers on the scantron card.
• Complete as many problems as you can.
• We will complete the test this week and go
over the solutions after your Chapter 11
Test next week before the EOGs.