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The Coordinate Plane

The Coordinate Plane. GEOMETRY LESSON 1-8. A has coordinates (3, 8). B has coordinates (0, –4). C has coordinates (–5, –6). State all answers in simplest radical form and to the nearest tenth. 12.4. 1. Find the distance between A and B to the nearest tenth.

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The Coordinate Plane

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  1. The Coordinate Plane GEOMETRY LESSON 1-8 A has coordinates (3, 8). B has coordinates (0, –4). C has coordinates (–5, –6). State all answers in simplest radical form and to the nearest tenth. 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 Chapter 1 TestFriday 1-8

  2. 1-8 The Coordinate Plane pp. 56-59 #53-78 Checkpoint Quiz pg. 59 #1-10

  3. 1-8 The Coordinate Plane pp. 56-59 #53-78 Checkpoint Quiz pg. 59 #1-10

  4. 1-8 The Coordinate Plane pp. 56-59 #53-78 Checkpoint Quiz pg. 59 #1-10

  5. Perimeter, Circumference, and Area GEOMETRY LESSON 1-9 The perimeter P of a polygon is the sum of the lengths of its sides.The areaA of a polygon is the number of square units it encloses. For special figures such as squares,rectangles, and circles, you can use formulas for perimeter (called circumference in circles) and area. 1-9

  6. Perimeter, Circumference, and Area GEOMETRY LESSON 1-9 1-9

  7. Margaret’s garden is a square 12 ft on each side. Margaret wants a path 1 ft wide around the entire garden. What will the outside perimeter of the path be? Because the path is 1 ft wide, increase each side of the garden by 1 ft. s = 1 + 12 + 1 = 14 Perimeter, Circumference, and Area GEOMETRY LESSON 1-9 Real World Connection P = 4sFormula for perimeter of a square P = 4(14) = 56 Substitute 14 for s. The perimeter is 56 ft. Quick Check 1-9

  8. . . . G has a radius of 6.5 cm. Find the circumference of G in terms of . Then find the circumference to the nearest tenth. C = 2 rFormula for circumferenceof a circle C = 2(6.5) Substitute 6.5 for r. C = 13 Exact answer C = 13 40.840704 Use a calculator. The circumference of G is 13 , or about 40.8 cm. Perimeter, Circumference, and Area GEOMETRY LESSON 1-9 Finding Circumference Quick Check 1-9

  9. Quadrilateral ABCD has vertices A(0, 0), B(9, 12), C(11, 12), and D(2, 0). Find the perimeter. Draw and label ABCD on a coordinate plane. Find the length of each side. Add the lengths to find the perimeter. AB = (9 – 0)2 + (12 – 0)2 = 92 + 122 Use the Distance Formula. =81 + 144 = 255 = 15 CD = (2 – 11)2 + (0 – 12)2 = (–9)2 + (–12)2 Use the Distance Formula. =81 + 144 = 255 = 15 Perimeter, Circumference, and Area GEOMETRY LESSON 1-9 Finding Perimeter in the Coordinate Plane BC = |11 – 9| = |2| = 2 Ruler Postulate DA = |2 – 0| = |2| = 2 Ruler Postulate 1-9

  10. (continued) Perimeter = AB + BC + CD + DA Perimeter, Circumference, and Area GEOMETRY LESSON 1-9 = 15 + 2 + 15 + 2 = 34 The perimeter of quadrilateral ABCD is 34 units. Quick Check 1-9

  11. To make a project, you need a rectangular piece of fabric 36 in. wide and 4 ft long. How many square feet of fabric do you need? A = bhFormula for area of a rectangle. A = (4)(3) Substitute 4 for b and 3 for h. Perimeter, Circumference, and Area GEOMETRY LESSON 1-9 Finding Area of a Rectangle Write both dimensions using the same unit of measurement. Find the area of the rectangle using the formula A = bh. 36 in. = 3 ft Change inches to feet using 12 in. = 1 ft. A = 12 You need 12 ft2 of fabric. Quick Check 1-9

  12. . . . In B, r = 1.5 yd. A = r2Formula for area of a circle. A = (1.5)2Substitute 1.5 for r. A = 2.25 The area of B is 2.25 yd2. Perimeter, Circumference, and Area GEOMETRY LESSON 1-9 Finding Area of a Circle Find the area of B in terms of . Quick Check 1-9

  13. Perimeter, Circumference, and Area GEOMETRY LESSON 1-9 Finding Area of an Irregular Shape Find the area of the figure below. Draw a horizontal line to separate the figure into three nonoverlapping figures: a rectangle and two squares. 1-9

  14. (continued) Find each area. Then add the areas. Perimeter, Circumference, and Area GEOMETRY LESSON 1-9 AR= bhFormula for area of a rectangle AR = (15)(5) Substitute 15 for b and 5 for h. AR= 75 AS = s2Formula for area of a square AS = (5)2Substitute 5 for s. AS = 25 A = 75 + 25 + 25 Add the areas. A = 125 The area of the figure is 125 ft2. Quick Check 1-9

  15. 1. Find the perimeter in inches. 2. Find the area in square feet. 3. The diameter of a circle is 18 cm. Find the area in terms of . 4. Find the perimeter of a triangle whose vertices are X(–6, 2), Y(8, 2), and Z(3, 14). 5. Find the area of the figure below. All angles are right angles. 81 cm2 Perimeter, Circumference, and Area GEOMETRY LESSON 1-9 A rectangle is 9 ft long and 40 in. wide. 296 in. 30 ft2 42 units 256 in.2 1-9

  16. Perimeter, Circumference, and Area GEOMETRY LESSON 1-9 (For help, go to the Skills Handbook page 757 and Lesson 1-8.) Simplify each absolute value. 1. |4 – 8| 2. |10 – (–5)| 3. |–2 – 6| 4.A(2, 3), B(5, 9) 5.K(–1, –3), L(0, 0) 6.W(4, –7), Z(10, –2) 7.C(–5, 2), D(–7, 6) 8.M(–1, –10), P(–12, –3) 9.Q(–8, –4), R(–3, –10) Find the distance between the points to the nearest tenth. Check Skills You’ll Need 1-9

  17. 6. d = (x2 – x1)2 + (y2 – y1)2 d = (10 – 4)2 + ( – 2 –(– 7))2 d = 62 + 52 d = 36 + 25 = 61 To the nearest tenth, WZ = 7.8. 7. d = (x2 – x1)2 + (y2 – y1)2 d = (– 7 – (– 5))2 + (6 – 2)2 d = (–2)2 + 52 d = 4 + 16 = 20 To the nearest tenth, CD = 4.5. Perimeter, Circumference, and Area GEOMETRY LESSON 1-9 Solutions 1. | 4 – 8 | = | –4 | = 4 2. | 10 – (–5) | = | 10 + 5 | = | 15 | = 15 3. | –2 – 6 | = | –8 | = 8 4. d = (x2 – x1)2 + (y2 – y1)2 d = (5 – 2)2 + (9 – 3)2 d = 32 + 62 d = 9 + 36 = 45 To the nearest tenth, AB = 6.7. 5. d = (x2 – x1)2 + (y2 – y1)2 d = (0 – (–1))2 + (0 – (–3))2 d = 12 + 32 d = 1 + 9 = 10 To the nearest tenth, KL = 3.2. 1-9

  18. Perimeter, Circumference, and Area GEOMETRY LESSON 1-9 Solutions (continued) 8. 9. d = (x2 – x1)2 + (y2 – y1)2 d = (–12 – (–1))2 + (–3 – (–10))2 d = (–11)2 + 72 d = 121 + 49 = 170 To the nearest tenth, MP = 13.0. d = (x2 – x1)2 + (y2 – y1)2 d = (–3 – (–8))2 + (–10 – (–4))2 d = 52 + (–6)2 d = 25 + 36 = 61 To the nearest tenth, QR = 7.8. 1-9

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