1. Geometry 13.5 The Midpoint Formula

2. The Midpoint Formula The midpoint of the segment that joins points (x 1,y 1 ) and (x 2,y 2 ) is the point (-4,2) (6,8) (1,5)

3. How does it work? 48 Find the coordinate of the Midpoint of BC. 12 7 ● 1 4 C ● AB 12 + 4 2, 7 + 1 2 (8,4) ● ● B (12,7) C (4,1) Midpoint:

4. Exercises 1. A (3,5) B (7,-5) midpoint: 3+7 2, 5+(-5) 2 (5,0) 2. A (0,4) B (4,3) midpoint: 0+4 2, 4+3 2 (2, ) 7 2 Try #1-#3!! 3. M (3,5) A (0,1) B (x,y)

5. Exercises 3. M (3,5) A (0,1) B (x,y) (6,9) This is the midpoint To find the coordinates of B : x-coordinate: 3 = 0 + x 2 6 = 0 + x x = 6 y-coordinate: 5 = 1 + y 2 10 = 1 + y y = 9

6. Exercises 4. A (p,g) B (p + 4,g) midpoint: 2p+4 2, 2g 2 (p + 2,g) Do #5 and #6 on your own and check answers below: 5.k 2 m 2, - 6. Point B: (6,1)

7. 7. Given points A (5,2) and B(3,-6) show that P (0,-1) is on the perpendicular bisector of AB.. ● ● In order to be on the perpendicular bisector, point P would have to be on the segment that is both perpendicular to AB and goes through it’s midpoint. A B Slope of AB: m = 2+6 (5,2) (3,-6) 5-3 ● (0,-1) P = 4 Midpoint of AB: 5+3 2, 2+(-6) 2 (4,-2) ● M Slope of PM: m = -2+1 4-0 = -¼ (4,-2) Perpendicular Let me explain method #2.

8. Homework pg. 545 WE #1-9 odd, 11,12,13, 17,19 Reminder: Makeups today 3:10