Mastering Midpoints in Coordinate Geometry

1. Applied Geometry Lesson 2-5 Midpoints Objective: Learn to find the coordinates of the midpoint of a segment

2. Example • Where would the midpoint between B and A be located? • Between B and C? Coordinate 3 Coordinate -2

3. Theorem • Theorem 2-5: • On a number line, the coordinate of the midpoint of a segment whose endpoints have coordinates a and b is

4. Example • Find the coordinate of the midpoint of • Find the coordinate of the midpoint of = -6.5 or –6 1/2 = -2

5. Your Turn • Find the coordinate of the midpoint of

6. Theorem 2.6 • On a coordinate plane, the coordinates of the midpoint of a segment whose endpoints have coordinates (x1 , y1) and (x2 , y2) are

7. Example • Find the coordinates of M, the midpoint of JK, given endpoints J(2, -9) and K (8, 3) Sketch a picture (will help you later). K (8, 3) J (2, -9) M (?, ?) = (5, -3)

8. Your Turn • Find the coordinates of N, the midpoint of VW, given the endpoints V(-4, -3) and W (6, 11) • Find the coordinates of Q, the midpoint of PR, given the endpoints P(-5, 1) and R(2, -8) N (?, ?) V (-4, -3) W (6, 11) Q (?, ?) R (2, -8) P (-5, 1)

9. Example • Suppose G (8, -9) is the midpoint of FE and the coordinates of E are (18, -21). Find the coordinates of F. E (18, -21) G (8, -9) F (?, ?) Use the midpoint formula, but fill in what you know. (2) (2) (2) (2) 18 + x = 16 -21 + y = -18 Solve: F (-2, 3) x = -2 y = 3

10. Your Turn • Suppose K (-10, 17) is the midpoint of IJ and the coordinates of J are (4, 12). Find coordinates of I. J (4, 12) K (-10, 17) I (?, ?) 12 + y = 34 4 + x = -20 x = -24 y = 22 I (-24, 22)

11. Your Turn • Suppose S (3, -3/4) is the midpoint of RT and the coordinates of T are (-2, 6). Find the coordinates of R T (-2, 6) S (3, -3/4) R (?, ?) (2) (2) 2 -2 + x = 6 x = 8

12. Homework • Pg. 79 1 – 13 all, 14 – 42 E