1. 1.5 – Midpoint

2. Midpoint: Point in the middle of a segment A B M

3. Ex 1: Find the midpoint of the segment. M M 1

4. Ex 2: Find the midpoint of the numbers without a number line. a.10 and 150 b.34 and 72 c.How did you find the midpoint? 10+150 2 = 80 34+72 2 = 53 Added them and then divided by 2

5. Ex 3: Find the midpoint of AB using a coordinate plane. a. A(5, 6) and B(1, 2) A(5, 6) M(, ) B(1, 2) A B M 34

6. b. A(–5, 6) and B(1, –2) A(-5, 6) M(, ) B(1, -2) A B M -22

7. c. Look and compare the x-coordinates then compare the y-coordinates. How can you find the midpoint of any segment without drawing a graph? Add the x’s then divide by 2 Add the y’s then divide by 2

8. Midpoint Formula:

9. Ex 4: Use the formula to find the midpoint of A(–4, 3) and B(–8, –9). x1x1 y1y1 x2x2 y2y2

10. Ex 5: Given the midpoint, M, of the segment, find the indicated measures.

11. a. MZ = ___________ x + 2 = 2x – 3 2 = x – 3 5 = x 2(5) – 3= 7

12. b. PR = ___________ 5x – 7 = 3x + 1 2x – 7 = 1 2x = 8 x = 4 5(4)-7 = 13 13+13 = 26

13. Ex 6: Given the midpoint and one endpoint, find the other endpoint.

14. A (, ) M B A M (2, 1) B (1, 4) 3-2

15. A (4, 4) M (-1, -2) B (, ) -6-8

16. A (, ) M (6, 5) B (7, 8) 52

17. A (-1, 2) M (1, 0) B (, ) 3-2