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18.13 Graphing rigid motions Let triangle ABC be formed by A( 4, 2), B( 4, 1), and C( 1, 1). Graph ^ABC and its image under the following combinations of transformations: (a) Reflect across the y axis and then move to the right 4 spaces. (b) Rotate 90 clockwise around the origin then move up 3 spaces. (c) Reflect across y 2 then move up 2 spaces and to the left 3 spaces.

(d) Reflect across the x axis and then reflect across the y axis. (e) Rotate 90 counter-clockwise around the origin and then reflect across x

Fig. 6-4



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Fig. 6-5

CHAPTER 14: Payroll Solution: Salaries Expense 414* FICA Social Security Payable 25.67 FICA Medicare Payable 6.00 Federal Income Tax Payable 47.00 Hospitalization Payable 7.20 Salaries Payable 328.13 *40 hours times $9 = $360 (regular pay) 4 hours times $13.50 = $54 (overtime pay) $360 + $54 = $414 (total pay)

Thus, the two circles shown in Fig. 6-5 are concentric circles. AB is a tangent of the inner circle and a chord of the outer one. CD is a secant of the inner circle and a chord of the outer one.

Two circles are equal if their radii are equal in length; two circles are congruent if their radii are congruent. Two arcs are congruent if they have equal degree measure and length. We use the notation mAC to denote measure of arc AC.





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If a chord divides a circle into two equal parts, then it is a diameter. (This is the converse of Principle 1.)

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Fig. 6-6

PRINCIPLE 3:

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A point is outside, on, or inside a circle according to whether its distance from the center is greater than, equal to, or smaller than the radius.

Solved Problem 14.3 Based on the information in Solved Problem 14.2, what is the entry to record the employer s payroll tax if it is assumed the state tax rate is 4 percent and the federal unemployment rate is 0.8 per cent (Prior to payroll) earnings to date = $5,100. Solution: Payroll Tax Expense 51.54 FICA Social Security Payable 25.67 FICA Medicare Payable 6.00 Federal Unemployment Insurance Payable 3.31 State Unemployment Insurance Payable 16.56

F is outside circle O in Fig. 6-6, since FO is greater in length than a radius. E is inside circle O since EO is smaller in length than a radius. A is on circle O since AO is a radius.

Fig. 6-7

Fig. 6-8

Thus in circle O of Fig. 6-8, if AC > CB, then j 1 > j 2. (Principles 6 and 7 are converses of each other.)

Thus in circle O of Fig. 6-9, if AB > AC, then AB > AC. (Principles 8 and 9 are converses of each other.)

Fig. 6-9

Fig. 6-10

15

PRINCIPLE 10:

Thus in circle O of Fig. 6-10, if CD ' AB, then CD bisects AB, AB, and ACB. A proof of this principle is given in 16.

PRINCIPLE 11:

Thus in circle O of Fig. 6-11, if PD is the perpendicular bisector of AB, then PD passes through center O.

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Fig. 6-11

Fig. 6-12

In This :

13: In the same or congruent circles, chords that are equally distant from the center are congruent.

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