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

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

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

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

Your Turn Find the coordinate of the midpoint of

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

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)

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) P (-5, 1) Q (?, ?) R (2, -8)

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

Your Turn I (-24, 22) J (4, 12) 12 + y = 34 4 + x = -20 x = -24 y = 22 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)

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

Homework Pg. 79 1 – 13 all, 14 – 42 E