MATHPOWER TM 10, WESTERN EDITION Chapter 6 Coordinate Geometry 6.2 6.2.1.

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Presentation transcript:

MATHPOWER TM 10, WESTERN EDITION Chapter 6 Coordinate Geometry

Determine the midpoint of the following line segment. 6 Note that adding the two end points of the line segment, then dividing by 2, produces the same result: (1 + 11) ÷ 2 = 6 M(3, 4) B(5, 4)A(1, 4) Horizontal Line Segments: To find the x-coordinate of the midpoint, divide the sum of the x-coordinates by 2. Vertical Line Segments: To find the y-coordinate of the midpoint, divide the sum of the y-coordinates by 2. M x = 3 C(5, -2) M(5, 1) M y = Finding the Midpoint of Vertical and Horizontal Lines Find the midpoint AB and BC.

Finding the Midpoint of a Line Segment A (4, 5) B (-4, -3) C (4, -3) BC = Midway is 4 units. This is an x-coordinate of 0. AC = Midway is 4 units. This is a y-coordinate of 1. Therefore, the midpoint is (0, 1). 8 units M x = 0 M y = 1 M(0, 1) 6.2.3

The midpoint (M) is the middle of a given line segment. The midpoint formula is The Midpoint Formula

Find the midpoint of the line segment with endpoints A(2, 8) and B(6, 12). M (AB) = (4, 10) (x 1, y 1 )(x 2, y 2 ) Using the Formula to Find the Midpoint of a Line Segment

Find the coordinates of B of the line segment AB. A is (2, 3) and the midpoint of AB is M(4, 7). The midpoint formula consists of two parts: 1. the x-coordinate of the midpoint 2. the y-coordinate of the midpoint Find the x-coordinate: Find the y-coordinate: x + 2 = 8 x = 6 y + 3 = 14 y = 11 B (6, 11) Using the Midpoint Formula to Find the Endpoint 6.2.6

Pages 261 and 262 1, 3, 5, 10, 11, 13, 15, 19, 22, 25a, 35 Suggested Questions: 6.2.7