Geometry Proof Unit The Distance Formula The distance formula is based on the Pythagorean Theorem, a2 + b 2 = c 2 . If you rearrange the formula: c = a 2 + b 2 Find the distance between (1, 3) and (5, 8). Plot the points. Draw segments to form a right triangle. length of a: 5 – 1 = 4

length of b: 8 – 3 = 5

length of c:

42 + 52 = 16 + 25 = 41 ≈ 6.4

The distance is about 6.4 units. Notice that when (x1, y1,) (x2, y2) are substituted for the coordinates of the endpoints, you have the Distance Formula: d =

2

( x2 − x1 )

2

+ ( y 2 − y1 ) .

Find the distance between each pair of points, to the nearest tenth. 1. A(2, 7) and B(5, 9)

2. C(5, 6) and D(8, 1)

3. E(–2, 6) and F(6, 8)

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Holt McDougal Algebra 1

Name ________________________________________ Date __________________ Class __________________ _________________________

4. G(3, –2) and H(10, 4)

________________________

5. J(–7, 3) and K(1, 4)

6. L(–2, 6) and M(8, 6)

8. M (−3, 5 ) and B (4, − 2 )

7. W(1, 14) and Y(5, 6)

9. G (−4, − 9 ) and H (0, 8 )

________________________

10. T (3, −2 ) and X (12, − 7 )

Each unit on the map of a neighborhood represents one mile. 11. Find the distance between the fire department and Fire 1, to the nearest tenth of a mile. ___________________________

12. Find the distance between the fire department and Fire 2, to the nearest tenth of a mile. ___________________________

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Holt McDougal Algebra 1

Review for Mastery 3 1. 4

Reading Strategies

1 2. 2

3. 4

2 4. − 5

5. −2

6. 3

1 7. 2

4 8. − 3

9.

1. 4 2. Possible answer: (−1, 6) 3. 2 5) 2 5. 5 7. horizontal

1 4

4. (−4, 1) and (6, 6. 0

LESSON 5–5 Practice A

Challenge

1. 2, 8, 1, 3, 10, 4, 5, 2

1.

2. (3, 2) 3. (3, 4) 3+x 4. 7 = 2 14 = 3 + x 11 = x

6+y 2 8=6+y 2=y 4=

(11, 2)

5. (1, 2) 6. 4, 1, 5, 1, 3, 4, 9, 16, 25, 5 7. ≈ 4.5 8. ≈ 6.4

2. Slope of AB = Slope of BC = 2

9. ≈ 11.3 miles

4. Slope of AB = 2; Slope of BD = 3

Practice B

5. Points A, B, and C lie on a line if the slopes of AB, BC and AC are equal. 6. 3%

1. (7, 2)

7. 300 feet

8. a. 6%

3.

b. No; the uphill grade is positive and the downhill grade is negative. 9. $2

( −2, − 2)

6. (4, 1)

7. ≈ 8.9

8. ≈ 9.9

9. ≈ 17.5

10. ≈ 10.3

2. −0.2; the number of pounds of flour used per day.

Practice C

3. 20 5. J

6. A

7. G

12. ≈ 8.1 miles

1" ! 13. # 9, 5 $ 2& %

1. 12; the number of kits assembled per day.

4. B

4. (6, 1)

5. (1, 11)

11. ≈ 7.2 miles

Problem Solving

1" ! 2. # 3, 2 $ 2& %

1. (4, 1)

2. (5, 4)

! 1 1" 3. $ − , − % & 4 4'

4. ( −2, 2)

!1 " 5. $ , − 8 % &2 '

6.

7. ≈ 5.8

( −2,9 )

8. ≈ 21.1

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Holt McDougal Algebra 1