Geometry
Notes
Name_________________________
Warm Up
1. What would be another way to write FG ?
2. Point S is between R and T on RT. Solve the equation. Then find RS and ST.
RS = 2x – 8
ST = 3x – 10
RT = 17
3. Find DE.
63
D
E
F
51
Today, we will


Define midpoint and bisector
Learn and apply the midpoint and distance formula
Midpoint and Distance Formulas
Lengths are equal
A
B
C
D
Segments are congruent
AB = CD
AB  CD
“is equal to”
“is congruent to”
A _____________________ divides a segment into two congruent segments.
A ____________________________________ is anything that intersects the segment at the midpoint.
C
M
A
M
M is the midpoint
B
A
B
D
CD is a segment bisector of AB
Example 1
In the diagram RT bisects UV at point S.
US = 42.5 cm. Find UV.
V
T
S
R
U
Example 2
If M is the midpoint of CD find the length of CM.
7x - 2
6x + 4
C
M
D
Midpoint Formula
 x1  x 2 y1  y 2
,

2
2




Example 3
a. The endpoints of GH are G(2, –4) and H(3, 3). Find the coordinates of the midpoint M.
b. The endpoints of AB are A(3, 5) and B(7, –9). Find the coordinates of the midpoint M.
c. The midpoint of XY is M(1, 2). One endpoint is X(4, 1). Find the coordinates of endpoint Y.
d. The midpoint of JK is M(6, 3). One endpoint is J(4, –2). Find the coordinates of endpoint K.
Distance Formula
AB  (x 2  x 1 ) 2  (y 2  y 1 ) 2
Example 4
Use the distance formula to find the distance between the two given points.
a. (2, –6), (5, –2)
b. (4, 9), (12, 3)
c. (2, 3), (4, –1)
d. (–3, 2), (1, –4)