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 mg remains after 36 years, what was the size of the initial sample?

about 15.5 ft 16.yes 18.no 20.no 22.yes ALGEBRA 1 LESSON 11-2 pages 587–590 Exercises no a.6 5 ft b.80.5 ft 2 34.no 11-2

44.a.6.9 ft b.89.2 ft 2 c.981 watts 46.a.Answers may vary. Sample: 5, 20, 5 b.5 units 2 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. ALGEBRA 1 LESSON yes lb a.These lengths could be 2 legs or one leg and the hypotenuse. b.about 12.8 in. or 6 in. 11-2

ALGEBRA 1 LESSON You are in Brazil; you are south of the equator; if you are south of the equator you are in Brazil; false units

Prentice Hall Lesson 11.3 EQ: What is the distance formula? Midpoint formula? Toolbox: The Distance Formula: The distance “d” between any two points (x 1, y 1 ) and (x 2, y 2 ) is d = √(x 2 – x 1 )² + (y 2 – y 1 )² The Midpoint Formula: The midpoint of a line segment with endpoints A(x 1, y 1 ) and B(x 2, y 2 ) is: (, ) x 1 + x 2 y 1 + y 2 2 2

d = (9 – 6) 2 + [–4 – (–9)] 2 Substitute (9, –4) for (x 2, y 2 ) and (6, –9) for (x 1, y 1 ). Find the distance between F(6, –9) and G(9, –4). ALGEBRA 1 LESSON 11-3 d = ( x 2 – x 1 ) 2 + (y 2 – y 1 ) 2 Use the distance formula. d = Simplify within parentheses. d = 34Simplify to find the exact distance. The distance between F and G is about 5.8 units. d 5.8Use a calculator. Round to the nearest tenth. 11-3

Find the exact lengths of each side of quadrilateral EFGH. Then find the perimeter to the nearest tenth. ALGEBRA 1 LESSON 11-3 EF =[4 – (–1)] 2 + (3 - 5) 2 =5 2 + (–2) 2 = =29 FG =(3 – 4) 2 + (–2 – 3) 2 =(–1) 2 + (–5) 2 = =26 GH =|–2 – 3| = 5 EH =[–2 – (–1)] 2 + (–2 – 5) 2 =(–1) 2 + (–7) 2 = = The perimeter = units.

ALGEBRA 1 LESSON 11-3 Find the midpoint of CD.,=,Substitute (–3, 7) for (x 1, y 1 ) and (5, 2) for (x 2, y 2 ) x 1 + x 2 2 y 1 + y 2 2 (–3) =, Simplify each numerator = 1, 4Write as a mixed number The midpoint of CD is M 1,

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? ALGEBRA 1 LESSON 11-3,=,Substitute (–3, 5) for (x 1, y 1 ) and (4, –3) for (x 2, y 2 ). 5 + (–3) 2 x 1 + x 2 2 y 1 + y 2 2 (–3) The center of the circle is at, =, =,

1.Find the distance between M(2, –1) and N(–4, 3) to the nearest tenth. 2.Find the distance between P(–2.5, 3.5) and R(–7.5, 8.5) to the nearest tenth. 3.Find the midpoint of AB, A(3, 6) and B(0, 2). 4.Find the midpoint of CD, C(6, –4) and D(12, –2). 5.Find the perimeter of triangle RST to the nearest tenth of a unit. ALGEBRA 1 LESSON units (9, – 3) (1, 4)

8 th 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.