Distance Between Two Points

Chapter 6 Coordinate Geometry 6.1 Distance Between Two Points 6.1.1 MATHPOWERTM 10, WESTERN EDITION

Length of a Line Segment The length of a horizontal line segment (parallel to the x-axis) can be calculated by taking the absolute value of the differences of the x-coordinates. E.g. Determine the distance between A(-3,2) and B(2, 2). Length of AB = | 2 - -3 | = | 5 | = 5 B(2, 2) A(-3, 2) In general, the length of a line segment parallel to the x-axis is: Length AB = | x2 - x1 | 6.1.2

Length of a Line Segment The length of a vertical line segment ( parallel to the y-axis) can be calculated by taking the absolute value of the differences of the y-coordinates. E.g. Determine the distance between A(-3,2) and B(-3, -2). Length of AB = | 2 - -2 | = | 4 | = 4 A (-3,2) In general, the length of a line segment parallel to the y-axis is: B(-3, -2) Length of AB = | y2 - y1 | 6.1.3

Length of a Line Segment The length of any oblique line may be found using the Pythagorean Theorem. Find the length AB. CB = | -3 - 2 | AC = | 4 - -4 | = | -5 | = 5 = | 8 | = 8 A(-3, 4) (AB)2 = (AC)2 + (CB)2 8 = 82 + 52 = 64 + 25 = 89 5 AB = √ 89 = 9.43 B(2, -4) C (-3, - 4) The length of AB is 9.43. 6.1.4

Deriving the Distance Formula P2(x2 , y2 ) c 2 = a 2 + b 2 (P1 D)2 + (P2 D)2 (P1P2)2 = P1(x1 , y1 ) = (x2 - x1)2 + (y2 - y1)2 D(x2 , y1 ) Distance Formula P1P2 6.1.5

Using the Distance Formula to Find the Length of a Line Find the distance between A(4, 2) and B(3, -5). x1 , y1 x2 , y2 The length of AB is 7.1. 6.1.6

Assignment Suggested Questions: Pages 256 and 257 1, 3, 5, 7, 15, 20a, 25ab 6.1.7

Distance Between Two Points

Distance Between Two Points

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