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EXAMPLE 1

A replica of the Parthenon, a temple in ancient Greece, was built in Nashville, Tennessee, in 1897. The diagram below shows the approximate dimensions of two adjacent rooms inside the replica. You can find the total area in two ways as shown in Example 1. EXAMPLE 1. Finding a Combined Area.

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EXAMPLE 1

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  1. A replica of the Parthenon, a temple in ancient Greece, was built in Nashville, Tennessee, in 1897. The diagram below shows the approximate dimensions of two adjacent rooms inside the replica. You can find the total area in two ways as shown in Example 1. EXAMPLE 1 Finding a Combined Area Architecture

  2. Two methods can be used to find the total area of the two rooms. EXAMPLE 1 Finding a Combined Area METHOD 1 Find the area of each room, and then find the total area. Area = 63(44) + 63(98) = 2772 + 6174 = 8946 square feet

  3. (142) = 63 ANSWER The total area of the two rooms is 8946 square feet. EXAMPLE 1 Finding a Combined Area METHOD 2 Find the total length, and then multiply by the common width. Area = 63(44 + 98) = 8946 square feet

  4. a. –5(x + 10) b. 3[1 – 20 + (–5)] EXAMPLE 2 Using the Distributive Property = –5x + (–5)(10) Distributive property = –5x + (–50) Multiply. = –5x – 50 Simplify. = 3(1) – 3(20) + 3(–5) Distributive property = 3 – 60 + (–15) Multiply. = 3 + (–60) + (–15) Add the opposite of 60. = –72 Add.

  5. 1. 10 ( 12 + 22 ) = ( 34 ) = 10 340 ft2 = for Examples 1 and 2 GUIDED PRACTICE Use the distributive property to find the area of the figure. Find the total length, and then multiply with common width. Area

  6. 2. 14 ( 3 + 9 ) = ( 12 ) = 14 168 m2 = for Examples 1 and 2 GUIDED PRACTICE Use the distributive property to find the area of the figure. Find the total length, and then multiply with common width. Area

  7. –2(5 + 12) 3. for Examples 1 and 2 GUIDED PRACTICE Use the distributive property to evaluate or write an equivalent expression. = –2(5) + (–2)(12) –2(5 + 12) Distributive property = –10 + (–24) Multiply. = –34 Add.

  8. –4(–7 – 10) 4. for Examples 1 and 2 GUIDED PRACTICE Use the distributive property to evaluate or write an equivalent expression. = –4(–7) – (–4)(–10) –4(–7 – 10) Distributive property = 28 + 40 Multiply. = 68 Add.

  9. 2(w – 8) 5. for Examples 1 and 2 GUIDED PRACTICE Use the distributive property to evaluate or write an equivalent expression. = 2w – (2)(8) 2(w – 8) Distributive property = 2w – (16) Multiply. = 2w – 16 Simplify.

  10. –8(z + 25) 6. = –8z + (–200) for Examples 1 and 2 GUIDED PRACTICE Use the distributive property to evaluate or write an equivalent expression. = –8z + (–8)(25) –8(z + 25) Distributive property Multiply. = –8z – 200 Simplify.

  11. 3x + 4x a. –9y + 7y + 5z b. EXAMPLE 3 Combining Like Terms = (3 + 4)x Distributive property = 7x Add inside grouping symbols. = (–9 + 7)y + 5z Distributive property = –2y + 5z Add inside grouping symbols.

  12. a. 2(4 + x) + x b. –5(3x – 6) + 7x EXAMPLE 4 Simplifying an Expression = 8 + 2x + x Distributive property = 8 + 3x Combine like terms. = –15x + 30 + 7x Distributive property = –8x + 30 Combine like terms.

  13. 2(x + 4) + 3x – 5 7. + (–5) = 5x + 8 for Examples 3 and 4 GUIDED PRACTICE Simplify the expression by combining like terms. = 2x + 8 + 3x – 5 2(x + 4) + 3x – 5 Distributive property Add. = 5x + 3 Combine like terms.

  14. 5y + 9z – 7 – 3y 8. = (5 – 3)y + 9z – 7 for Examples 3 and 4 GUIDED PRACTICE Simplify the expression by combining like terms. 5y + 9z – 7 – 3y Distributive property = 2y + 9z – 7 Combine like terms.

  15. –3(6x + 2y) + 22x 9. for Examples 3 and 4 GUIDED PRACTICE Simplify the expression by combining like terms. = –18x –6y + 22x –3(6x + 2y) + 22x Distributive property = 4x –6y Combine like terms.

  16. Sec. 2.8

  17. Give the coordinates of the point. A B C Point Ais 3 units to the right of the origin and 1.5 units up. So, the x-coordinate is 3 and the y-coordinate is 1.5. The coordinates of Aare (3, 1.5). Point Bis 3 units to the left of the origin and 2 units down. So, the x-coordinate is –3 and the y-coordinate is –2. The coordinates of Bare (–3, –2). EXAMPLE 1 Naming Points in a Coordinate Plane SOLUTION

  18. Point Cis 2 units up from the origin. So, the x-coordinate is 0 and the y-coordinate is 2. The coordinates of Care (0, 2). EXAMPLE 1 Naming Points in a Coordinate Plane

  19. Use the graph. Give the coordinates of the point. D for Example 1 GUIDED PRACTICE SOLUTION Point Dis 3 units to the right of the origin and 4 units down. So, the x-coordinate is 3 and the y-coordinate is –4. The coordinates of Dare (3, –4).

  20. Use the graph. Give the coordinates of the point. E for Example 1 GUIDED PRACTICE SOLUTION Point Eis 2.5 units to the left of the origin and 2 units up. So, the x-coordinate is –2.5 and the y-coordinate is 2. The coordinates of Dare (–2.5, 2).

  21. Use the graph. Give the coordinates of the point. F for Example 1 GUIDED PRACTICE SOLUTION Point Fis 3 units to the left of the origin. So, the x-coordinate is 0 and the y-coordinate is –3. The coordinates of Fare (0, –3).

  22. Plot the point and describe its location. (0 , –3) (4, –2) (–1, 2.5) C A B Begin at the origin, move 4 units to the right, then 2 units down. Point Alies in Quadrant IV. Begin at the origin, move 1 unit to the left, then 2.5 units up. Point Blies in Quadrant II. EXAMPLE 2 Graphing Points in a Coordinate Plane SOLUTION

  23. Begin at the origin, move 3 units down. Point Clies on the y-axis. EXAMPLE 2 Graphing Points in a Coordinate Plane

  24. On a field trip, students are exploring an archaeological site. They rope off a region to explore as shown. Identify the shape of the region and find its perimeter. The units on the scale are feet. EXAMPLE 3 Solve a Multi-Step Problem Archaeology

  25. x-coordinate ofA – l = x-coordinateofB –60 60 –30 –30 = = = EXAMPLE 3 Solve a Multi-Step Problem SOLUTION Notice that points A, B, C,and Dform a rectangle. Find the coordinates of the vertices. STEP1 A(–30, 20),B(30, 20),C(30, –20),D (–30, –20) STEP2 Find the horizontal distance from Ato Bto find the lengthl.

  26. y-coordinate ofA – w = y-coordinateofD 40 40 20 – (–20) = = = = 2(60) + 2(40) ANSWER The region’s perimeter is 200 units 10feet per unit =2000feet. EXAMPLE 3 Solve a Multi-Step Problem Find the vertical distance from Ato Dto find the width w. STEP3 STEP4 Find the perimeter: 2l + 2w = 200.

  27. (1, –2.5) (–3, 4) R S for Examples 2 and 3 GUIDED PRACTICE Plot the point and describe its location. Begin at the origin and move 3 units to the left, then 4 units up. Point R lies in Quadrant II. Begin at the origin and move 1 unit right, then 2.5 units down. Point S lies in Quadrant IV.

  28. (0.5 , 3) T (–3, 4) U for Examples 2 and 3 GUIDED PRACTICE Plot the point and describe its location. Begin at the origin and move 0.5 unit to the right, then 3 units up. Point T lies in Quadrant I. Begin at the origin and move 4 units to the left. Point U lies on the x-axis.

  29. ANSWER Answers may vary. Sample answer: Moving A and B to A(–30, 0) and B(30, 0), the perimeter is 160 units. Move points Aand Bin Example 3 to form a new rectangle. Find the perimeter. for Examples 2 and 3 GUIDED PRACTICE Plot the point and describe its location.

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