Name ________________________________________ Date __________________ Class __________________
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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5-37
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
