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We are already familiar with the types of accounts found in a service business that is, a business in which revenue comes from services rendered so we shall rst discuss the worksheet for such a business. The work sheet is usually prepared in pencil on a large sheet of ac counting stationery called analysis paper. On the worksheet, the ledger accounts are adjusted, balanced, and arranged in proper form for prepar ing the nancial statements. All procedures can be reviewed quickly, and the adjusting and closing entries can be made in the formal records with less chance of error.



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36. Then:

area(DEFC)

^BCF)

1 2 h(b 1 2 (3)(2 1 2 (6)(2 1 2 (3)(4

(b) Area of trapezoid ABHG Area of trapezoid BCJH Area of trapezoid ACJG Then area(^ABC)

string normalizespace(string )

br) 8) 4)

15. 18. area(ACJG) 18 15 18 15.

Note!

area(ABHG)

area(BCJH)

Many theorems of plane geometry can be proved with analytic geometry. The procedure for proving a theorem has two major steps, as follows: 1. Place each figure in a convenient position on a graph. For a triangle, rectangle, or parallelogram, place one vertex at the origin and one side of the figure on the x-axis. Indicate the coordinates of each vertex (Fig. 12-30).





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Triangle y C(c, h) h x c A (0, 0) y b x B(b, 0) x A (0, 0) y b B(b, 0) y D (0, h) h x x c A (0, 0) y Rectangle y C(b, h) D(c, h) h x b B(b, 0) C(b + c, h) Parallelogram

Fig. 12-30

2. Apply the principles of analytic geometry. For example, prove that lines are parallel by showing that their slopes are equal; or that lines are perpendicular by showing that their slopes are negative reciprocals of each other. Use the midpoint formula when the midpoint of a segment is involved, and use the distance formula to obtain the lengths of segments.

With the data for the income statement and bal ance sheet already proved out on the worksheet, these statements can be prepared more quickly.

12.21 Proving a theorem with analytic geometry Using analytic geometry, prove that the diagonals of a parallelogram bisect each other.

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Given: ~ABCD, diagonals AC and BD. To Prove: AC and BD bisect each other. Plan: Use the midpoint formula to obtain the coordinates of the midpoints of the diagonals Place ~ ABCD with vertex A at the origin and side AD along the x-axis (Fig. 12-31). Then the vertices have the coordinates A(0, 0), B(a, b), C(a c, b), and D(c, 0). a c b , R, and the midpoint of BD has By the midpoint formula, the midpoint of AC has the coordinates Q 2 2 a c b , R. Then the diagonals bisect each other, since the midpoints of both diagonals are the the coordinates Q 2 2 same point.

y B(a, b) C(a + c, b)

x A (0, 0) y D(c, 0)

Fig. 12-31

12.1. State the coordinates of each lettered point in Fig. 12-32. (12.1)

boolean contains(string, string)

Fig. 12-32

For a typical service business, we may suppose the worksheet to have eight monetary columns; namely, a debit and credit column for four groups of gures: trial balance, adjustments, income statement, and bal ance sheet. A ten-column work sheet also is used, consisting of: 1. Trial balance 2. Adjustments 3. Adjusted trial balance 4. Income statement, and 5. Balance sheet. The adjusted trial balance columns simplify the extension to the nancial statement columns. The steps for completing the worksheet are:

12.2. Plot each of the following points: A( 2, 3) B( 3, 2) C(0, 1) D( 3, 0) E(3, 4) F(11, 21) 2 2 G(0, 3) H(31, 0) 2 2), D(2,

(12.2)

12.3. Plot the following points: A(2, 3), B( 3, 3), C( 3, ABCD. 12.4. Plot the following points: A(4, 3), B( 1, 3), C( 3, and triangle BCD. 12.5. Find the midpoint of the segment joining (a) (0, 0) and (8, 6) (b) (0, 0) and (5, 7) (c) (0, 0) and ( 8, 12) (d) (14, 10) and (0, 0) (e) ( 20,

3), D(2,

3). Then find the area of parallelogram ABCD (12.3, 12.4) (12.5)

5) and (0, 0)

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