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Coordinate Plane y Axes (plural of axis) 0 x-axis 0 y-axis x Coordinate Plane y Origin x Coordinate Plane y Quadrants II I III IV x 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. Coordinates State the coordinates: 0A 0B 0C 0D 0E 0F (5,2) (-8,-5) (-3,5) (4,-7) (0,4) (-7,0) C E A F B D 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? 13 12 5 a 2 b2 c 2 52 122 c 2 25 144 c 2 169 c 2 169 c 2 13 c Distance formula 0 The distance between two points x1 , y1 and x2 , y2 on the coordinate plane (graph) can be found using the formula: d x2 x1 y2 y1 2 2 http://www.bsin.k12.nm.us/schools/BHS/math/joinmath/geometry/GEO1_3.pps#257,4,Slide 4 Practice Find the distance between R(–2, –6) and S(6, –2) to the nearest tenth. d= (x2 – x1)2 + (y2 – y1)2 d= (6 – (–2))2 + (–2 – (–6))2 d= 82 + (–8)2 d= 64 + 64 = 128 To the nearest tenth, RS = 11.3. Midpoint Formula In the coordinate plane, the coordinates of the midpoint of a segment whose endpoints have coordinates ( x1 , y1 ) and ( x2 , y2 ) are x1 x2 , y1 y2 . 2 2 Example: Find the midpoint between (-2, 5) and (6, 4) x1 y1 M= 2 6 , 5 4 2 2 M= 4 , 9 = 2, 9 2 2 2 x2 y2 Practice AB has endpoints (8, 9) and (–6, –3). Find the coordinates of its midpoint M. ( x1 + x2 2 8 + (–6) 2 = =1 2 2 , y1 + y2 2 ) 9 + (–3) 6 = =3 2 2 The coordinates of midpoint M are (1, 3). Homework The Coordinate Plane in Student Practice Packet (Page 7, #1-13)