The Coordinate Plane

The Coordinate Plane GEOMETRY LESSON 1-8 (For help, go to the Skills Handbook, pages 753 and 754.) Find the square root of each number. Round answers to nearest tenth. 1. 25 2. 17 3. 123 4. (m – n)25. (n – m)26.m2 + n2 7. (a – b)28. 9. Evaluate each expression for m = –3 and n = 7. Evaluate each expression for a = 6 and b = –8. a + b 2 a2 + b2 Quiz 1-5 to 1-9Friday Check Skills You’ll Need 1-8

a + b 2 6 + (–8) 2 9. = –2 2 = –1 = The Coordinate Plane GEOMETRY LESSON 1-8 Solutions 1. 25 = 52 = 5 2. 17 4.1232 = 4.1 3. 123 11.0912 = 11.1 4. (m – n)2 = (–3 –7)2 = (–10)2 = 100 5. (n – m)2 = –7 – (–3))2 = (7 + 3)2 =102 = 100 6.m2 + n2 = (–3)2 + (7)2 = 9 + 49 = 58 7. (a – b)2 = (6 – (–8))2 = (6 + 8)2 =142 = 196 8.a2 + b2 = (6)2 + (–8)2 = 36 + 64 = 100 = 10 1-8

1-7 Basic Constructionspp. 47-50 #3, 4, 6, 7, 10, 14, 18, 20-22, 28, 35, 36-38, 41-49

The Coordinate Plane GEOMETRY LESSON 1-8 1-8

Find the distance between R(–2, –6) and S(6, –2) to the nearest tenth. d =(x2–x1)2+(y2–y1)2Use the Distance Formula. d =(6 –(–2))2+(–2 –(–6))2Substitute. d =82+(–8)2Simplify. d =64+64 = 128 128 11.3137085 Use a calculator. The Coordinate Plane GEOMETRY LESSON 1-8 Finding Distance Let (x1, y1) be the point R(–2, –6) and (x2, y2) be the point S(6, –2). To the nearest tenth, RS = 11.3. Quick Check 1-8

How far is the subway ride from Oak to Symphony? Round to the nearest tenth. d =(x2–x1)2+(y2–y1)2Use the Distance Formula. d =(1 –(–1))2+(2 –(–2))2Substitute. d =22+42Simplify. = 20 d =4+16 20 4.472135955 Use a calculator. The Coordinate Plane GEOMETRY LESSON 1-8 Real World Connection Oak has coordinates (–1, –2). Let (x1, y1) represent Oak. Symphony has coordinates (1, 2). Let (x2, y2) represent Symphony. To the nearest tenth, the subway ride from Oak to Symphony is 4.5 miles. Quick Check 1-8

AB has endpoints (8, 9) and (–6, –3). Find the coordinates of its midpoint M. 8 + (–6) 2 2 2 The x–coordinate is = = 1 The midpoint has coordinates Midpoint Formula x1 + x2 2 y1 + y2 2 ( , ) Substitute 8 for x1 and (–6) for x2. Simplify. 6 2 The y–coordinate is = = 3 9 + (–3) 2 Substitute 9 for y1 and (–3) for y2. Simplify. The Coordinate Plane GEOMETRY LESSON 1-8 Finding the Midpoint Use the Midpoint Formula. Let (x1, y1) be A(8, 9) and (x2, y2) be B(–6, –3). The coordinates of midpoint M are (1, 3). Quick Check 1-8

Use the Midpoint Formula. Let (x1, y1) be D(1, 4) and the midpoint be (–1, 5). Solve for x2and y2, the coordinates of G. Use the Midpoint Formula. –2 = 1 + x2 10 = 4 + y2 Multiply each side by 2. 6 = y2 –3 = x2 1 + x2 4 + y2 –1 = ( , ) 5 = x1 + x2 y1 + y2 2 2 2 2 The Coordinate Plane GEOMETRY LESSON 1-8 Finding an Endpoint The midpoint of DG is M(–1, 5). One endpoint is D(1, 4). Find the coordinates of the other endpoint G. Find the x–coordinate of G. Find the y–coordinate of G. The coordinates of G are (–3, 6). Quick Check 1-8

The Coordinate Plane GEOMETRY LESSON 1-8 A has coordinates (3, 8). B has coordinates (0, –4). C has coordinates (–5, –6). 12.4 1. Find the distance between A and B to the nearest tenth. 2. Find BC to the nearest tenth. 3. Find the midpoint M of AC to the nearest tenth. 4.B is the midpoint of AD. Find the coordinates of endpoint D. 5. An airplane flies from Stanton to Mercury in a straight flight path. Mercury is 300 miles east and 400 miles south of Stanton. How many miles is the flight? 6. Toni rides 2 miles north, then 5 miles west, and then 14 miles south. At the end of her ride, how far is Toni from her starting point, measured in a straight line? 5.4 (–1, 1) (–3, –16) 500 mi 13 mi 1-8

Use the figure at right. NQ bisects DNB. 1. Construct AC so that ACNB. 2. Construct the perpendicular bisector of AC. 3. Construct RST so that RSTQNB. 4. Construct the bisector of RST. 5. Find x. 6. Find mDNB. Basic Constructions GEOMETRY LESSON 1-7 For problems 1-4, check students’ work. 17 88 1-7

The Coordinate Plane