1.1c: Midpoint ,Segment
Congruence, and Segment
Addition
CCSS
G-CO.1 Know precise definitions of angle, circle, perpendicular line,
parallel line, and line segment, based on the undefined notions of
point, line, distance along a line, and distance around a circular arc.
GSE
M(G&M)–10–9 Solves problems on and off the coordinate plane
involving distance, midpoint, perpendicular and parallel lines, or
slope
Midpoint
• The point that bisects a segment.
• Bisects?
splits into 2 equal pieces
12x+3
A
12x+3=10x+5
2x=2
x=1
10x+5
M
B
Segment Bisector
• A segment, ray, line, or plane that
intersects a segment at its midpoint.
k
A
M
B
Midpoint Formula
• Used for finding the
coordinates of the
midpoint of a segment
in a coordinate plane.
• If the endpoints are
(x1,y1) & (x2,y2), then
 Average , Average

of
 of
 x' s
y' s






Ex: Find the midpoint of JT
if J(-3, 5) & T(4,2).
x' s
-3 4

2
y's
52
2
1
 0 .5
2

7
 3 .5
2
0 . 5 ,3 . 5 
x’s
y’s
Ex. Find the midpoint of DC
and label it point A
A
 4  4 6  4 
A
,

2 
 2
0 2
A , 
2 2
A 0 , 1 
CA  DA
Ex: The midpoint of AB is M(2,4). One endpoint
is A(-1,7). Find the coordinates of B.
 x1  x 2 y 1  y 2 
,

  ( midpoint
2
2


x1  x 2
y1  y 2
2
2
 1  x2
)
4
2
7  y2
2
2
B
4
2
7  y2  8
 1  x2  4
y2  1
x2  5
B 5 ,1 
Ex: The midpoint of AB is M(-3,5).
One endpoint is A(4,6). Find the coordinates of B.
A major league baseball diamond is a square having side lengths 90 feet.
Overlay a rectangular coordinate system on the baseball diamond so that:
-the origin is at home plate
-the positive x-axis is along the first base line
-the positive y-axis is along the third base line.
i.
What are the coordinates of first, second, and third base?
ii. What is the distance from home plate to second base?
iii. If the right fielder is at (305, 10), how far is the right fielder from second base?
iv. Suppose you want to position the pitching mound at equal distances from
second base and home plate. What coordinates would the pitching mound
have?
v. The left fielder was at (15, 250) and threw a ball into the infield that was cut off
by the shortstop at (8, 120). The shortstop was in the middle between the
left fielder and pitcher. What are the coordinates of the pitcher?
Post. 2: Segment Addition
Postulate.
• If B is between A & C, then
AB + BC = AC.
• If AB + BC = AC, then B is
between A & C.
A
B
C
Seg. Add. Post. Example
• If J is between H and K and HJ=5x-3 ,
JK = 4x, HK = 8x, find HJ, JK, HK
• Ans: Draw a diagram
Example
• M is between L and N. Find each
measurement if:
LM = 4x+6 ,
LN = 5x+10
MN = 3x – 4
LM + MN = LN
4 x  6  3 x  4  5 x  10
LM =4(4)+6 = 22
MN = 3(4)-4 = 8
LN = 5(4)+10 = 30
7 x  2  5 x  10
2x  8
x4
Ex: if DE=2, EF=5, and
DE=FG, find FG, DF, DG, &
EG.
D
E
F
FG=2
DF=7
DG=9
EG=7
G
Assignment