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The Coordinate Plane Mrs. King Geometry Unit 1, Lesson 6

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Coordinate Plane Axes (plural of axis) 0 x-axis 0 y-axis x y

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Coordinate Plane Origin x y

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Coordinate Plane Quadrants x y III III IV

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Coordinates Plot and label the points: 0 A(4,7) 0 B(-3,5) 0 C(4,-7) 0 D(-6,-3) State the quadrant in which each point is graphed.

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Coordinates State the coordinates: 0 A 0 B 0 C 0 D 0 E 0 F A B C D E F (5,2) (-8,-5) (-3,5) (4,-7) (0,4) (-7,0)

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Distance in the coordinate plane Kayleigh walks to a friend’s house by traveling 5 blocks west and then 12 blocks north. She returns home later by cutting diagonally through her neighbors’ yards. What distance did she travel on her voyage home?

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Distance formula 0 The distance between two points and on the coordinate plane (graph) can be found using the formula:

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http://www.bsin.k12.nm.us/schools/BHS/math/joinmath/geometry/GEO1_3.pps#257,4,Slide 4

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d = 8 2 + (–8) 2 Find the distance between R(–2, –6) and S(6, –2) to the nearest tenth. To the nearest tenth, RS = 11.3. d = (x 2 – x 1 ) 2 + (y 2 – y 1 ) 2 d = (6 – (–2)) 2 + (–2 – (–6)) 2 d = 64 + 64 = 128 Practice

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Midpoint Formula M = Find the midpoint between (-2, 5) and (6, 4) Example: In the coordinate plane, the coordinates of the midpoint of a segment whose endpoints have coordinates and are. x1y1x2y2

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The coordinates of midpoint M are (1, 3). AB has endpoints (8, 9) and (–6, –3). Find the coordinates of its midpoint M. (, ) x 1 + x 2 2 y 1 + y 2 2 8 + (–6) 2 = = 1 2222 9 + (–3) 2 = = 3 6262 Practice

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Homework The Coordinate Plane in Student Practice Packet (Page 7, #1-13)

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Page 2. Midpoint Formula Coordinates of the midpoint: M = The midpoint is the average of the x’s and the average of the y’s New Vocabulary: Abscissa –

Page 2. Midpoint Formula Coordinates of the midpoint: M = The midpoint is the average of the x’s and the average of the y’s New Vocabulary: Abscissa –

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