1. Sec. 1 – 8 The Coordinate Plane Objectives: 1) Find the distance between 2 points on the coordinate plane. 2) Find the coordinate of the midpoint of a segment on the coordinate plane.

2. Coordinate Plane x-axis (Independent) y-axis (Dependent) Quad. I ( +, +) Quad. II ( -, +) Quad. III ( -, -) Quad. IV ( +, -) Ordered Pair: (x, y) A(2, -1) A

3. Graph the following equation. y = 3x + 1 2 methods –x/y chart –Slope-Intercept Form Slope y-intercept

4. Graphing and finding the distance Graph A(2, -2) & B(2, 6) Graph C(1, 2) & D(5, 6)

5. Distance Formula Distance Formula: The distance (d) between two points A(x 1, y 1 ) and B(x 2, y 2 ) is d AB = √(x 2 – x 1 ) 2 + (y 2 – y 1 ) 2

6. Ex.1: Find the distance between the following points. R(-2, 6) & S(4, 4) x1 y1 x2 y2 d RS = √(x 2 – x 1 ) 2 + (y 2 – y 1 ) 2 = √(4 – (-2)) 2 + (4 – 6) 2 = √(6) 2 + (-2) 2 = √36 + 4 = √40= 6.3

7. Find the distance between R(–2, –6) and S(6, –2) to the nearest tenth. Let (x 1, y 1 ) be the point R(–2, –6) and (x 2, y 2 ) be the point S(6, –2). To the nearest tenth, RS = 11.3. 128 11.3137085Use a calculator. d = (x 2 – x 1 ) 2 + (y 2 – y 1 ) 2 Use the Distance Formula. d = (6 – (–2)) 2 + (–2 – (–6)) 2 Substitute. d = 64 + 64 = 128 1-6 d = 82 + (–8) 2 Simplify.

8. Graphing the Midpoint Graph A(2, -2) & B(2, 6) Graph C(1, 2) & D(5, 6)

9. MidPoint formula Midpoint Formula: The coordinates of the midpoint M of AB with endpoints A(x1, y1) and B(x2, y2) are the following: x-coordinate of a point y-coordinate of a point x 2 + x 1 2 y 2 + y 1 2, () M

10. Ex.2: AB has endpts A(8, -9) & B(-6, 3). Find the coordinates of its midpt. x 2 + x 1 2 y 2 + y 1 2, M () x1 y1x2 y2 (-6) + 8 2 3 + (-9) 2, M () 2 2 -6 2, M () M(1, -3)

11. Ex.3: The midpt of DG is M(-1, 5). One endpt is D(1, 4). Find the coordinates of the other endpts. x 2 + x 1 2 X m = y 2 + y 1 2 y m = x m y m x1 y1 x 2 +1 2 -1 = (2) -2 = x 2 + 1 -3 = x 2 y 2 + 4 2 5 = (2) 10 = y 2 + 4 6 = y 2 G(-3, 6)

12. What have we learned??? Distance Formula Midpoint formula d AB = √(x 2 – x 1 ) 2 + (y 2 – y 1 ) 2 x 2 + x 1 2 y 2 + y 1 2, () M R(-2, 6) & S(4, 4) x1 y1 x2 y2