Transcript Chapter 1.3

Chapter 1.3-1.4
Midpoint Formula
Construct Midpoints
• Midpoint (of a segment) – the
point that splits the segment into
2 equal parts (where the segment
is cut)
A
Z
B
• If X is the midpoint of AC and XC =
10, how long is AX? AC?
With Algebra
Z is midpoint of MP. Find x.
3x
M
24 - x
Z
P
3x = 24 – x
+1x=
+ 1x
4x = 24
X = 6
Bisector (of a segment) – a line,
segment ray, or plane that
intersects a segment at the
midpoint (it does the cutting)
m
midpoint
A
Z
B
Hatch Marks – short slash markings that
show two or more segments are equal in
length
Urkle
Stephon
W
X
~
WX = YZ
Zack
Y
Z
Cody
Congruent - segments that have the same
measure (like equal)
Midpoint formula:
x2  x1
 xmidpoint
2
y2  y1
 ymidpoint
2
( xmidpoint , ymidpoint )
( x2, y2 )
( x1, y1 )
Find the midpoint whose endpoints are (2, -3) and (-14, 13)
y2  y1
 ymidpoint
2
x2  x1
 xmidpoint
2
14 + 2
= x midpoint
2
12
2

13 + 3
2
10
6
(6 , 5 )
= y midpoint
2

( xmidpoint , ymidpoint )
5
( x2, y2 )
( x1, y1 )
Find the midpoint whose endpoints are (1, -2) and (-17, 16)
x2  x1
 xmidpoint
2
17
+
16 + 2
1
= x midpoint
2
16
2

y2  y1
 ymidpoint
2
8
= y midpoint
2
14
2

(8 , 7 )
( xmidpoint , ymidpoint )
7
What if you are missing an
endpoint ?
• When given the midpoint and
one endpoint, set up the formula
just as before.
(-2,2)
(-3,-5)
( ?, ?)
M(-3, -5) is the midpoint of RS. If S has a coordinates
(-2, 2), find the coordinates of R.
(2)
 2 + x1
( x2, y2 )
( xm, ym )
(x1, y1)
R
(x1, y1)
S
M(-3, -5)
= 3 (2)
(-2, 2)
2 + y1y1
(2)
2
2  x1  6
2
2
5 (2)
=
2
2  y1  10
2
2
y1  12
x1  4
(4 ,12)
M(4, 2) is the midpoint of RS. If S has a coordinates (5, -2),
find the coordinates of R.
(x1, y1)
R (x1, y1)
(2)
5 + x1
( xm, ym )
( x2, y2 )
M(4, 2)
S (5,-2)
= 4 (2)
(2) 2 +
2
5  x1 
5
y1
2 (2)
=
2
2  y1  4
8
5
2
2
y1  6
x1  3
(3 ,
6
)
Book p.41-44
The End!