1. If we have a line on a graph, how can we determine where the midpoint of that line is? Straight Line Segment Midpoint of Line (x, y) = ? Endpoints

2. Determine the midpoint of a line segment with endpoints A(10, 2) and B(6, 8). A B To find the midpoint, translate the line to the origin, so it’s easier. x: translated left 6 units y: translated down 8 units B: (6, 8) B’: (6 – 6, 8 – 8) = (0, 0) A: (10, 2) A’: (10 - 6, 2 – 8) = (4, -6) B’

4. The midpoint of A’B’ is (2, -3) Now we need to translate this point using the operations we used to translate the 2 points in the beginning. (2, -3) x-coordinate of midpoint M 2 + 6 = 8 y-coordinate of midpoint M -3 + 8 = 5 Therefore, the coordinates of the midpoint of the original line is: M = (8, 5).

5. F=? Rise = -1.5 – (-3.25) = + 1.75 Run = 0.5 – 2.125 = - 1.625 To go from E to M, we added 1.75 to the value of y, and subtracted 1.625 from the value of x. To go from M to F, we need to add 1.75 to the value of y, and subtract 1.625 from the value of x of M.

6. F=? + 1.75 - 1.625 + 1.75 - 1.625

7. A waste management company is planning to build a landfill in a rural area. To balance the impact on the two closest towns, the company wants the landfill to be the same distance from each town. On a coordinate map of the area, the towns are at A(1, 8) and B(5, 2). Describe all the possible locations for the landfill.

8. B (5, 2) All these points are the same distance from A and B This perpendicular bisector is at 90 o to the line AB Possible Locations for the landfill are determined by points that are on the line We need to determine an equation for this line We need: slope and y-intercept

9. B (5, 2)

11. pg. 79 # 4cf, 5, 6, 7, 9, 14, 16, 19