Mathematics III: Geometry Pineda, KWP

4th Quarter – Plane Coordinate Geometry Copyright 2013

THE MIDPOINT FORMULA Midpoint M lies between the endpoints of AB.

EXERCISE: Find the coordinates of the midpoint of the following endpoints of a given segment. 1. (2 , 3) and (5 , 7)?

The Midpoint Formula If P1 (x1, y1) and P2 (x2 , y2) are any two points in a coordinate plane, then the

midpoint M of has coordinates

Mathematics III: Geometry Pineda, KWP

4th Quarter – Plane Coordinate Geometry Copyright 2013

2. (3 , 7) and (-6 , 1)

Given the midpoint M, find the unknown. 3. (2 , b) and (a , -1) ; M (-1 , 1) TRY THE FOLLOWING: A. Find the coordinates of the midpoint of the following endpoints of a segment.

1. (4 , 0) and (8 , 0)

2. (2 , -1) and (6 , 3)

3. (7 , 4) and (5 , -10)

4. (-3 , -5) and (-7 , 9)

5. (-4 , -7) and (-9 , 8)

16. (3 , -6) and (3 , 8)

17. (4 , 8) and (2 , -8)

18. (-5 , -4) and (-11 , -22)

19. (-4 , -6) and (-2 , -9)

20. (7 , -9) and (4 , 8)

11. (-42 , -53) and (28 , -19)

12. (1.4 , -2.3) and (3.6 , 1.1)

13. (27 , -36) and (77 , -102)

14. (6 , 3) and (-1 , -3)

15. (-3 , 1) and (3 , -2)

Mathematics III: Geometry Pineda, KWP

4th Quarter – Plane Coordinate Geometry Copyright 2013

B. If M is the midpoint of AB, solve for the coordinates of B. BIBLIOGRAPHY: Jose Dilao, S. & Bernabe, J. (2009). Geometry: Textbook for Third Year. SD Publications Inc., Araneta Avenue, Quezon City. Mercado, et. al. (2003). Next Century Mathematics Third Year High School: Geometry. Phoenix Publishing House Inc.,

Quezon Avenue, Quezon City.

1. M(2 , 3) , A(7 , 1)

2. M(1 , -2) , A(3 , -6)

3. M(1 , 6) , A(-2 , 5)

4. M(-1 , 5) , A(3 , 8)

5. M(0 , 0) , A(-3 , -1)

6. M(4 , 3/2) , A(9 , -2)

7. M(4 ½ , -1/2) , A(5 , -8)

4. M(3 ½ , -7) , A(3 , -8)

5. M(1 ½ , 1/2) , A(5 , -5)