1. 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

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

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 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)

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 – 13 all, 14 – 42 E