1-3 Distance and Midpoint.notebook - Mrs. Foy's Classroom
1-3 Distance and Midpoint.notebook - Mrs. Foy's Classroom
1-3 Distance and Midpoint.notebook - Mrs. Foy's Classroom
Create successful ePaper yourself
Turn your PDF publications into a flip-book with our unique Google optimized e-Paper software.
13 <strong>Distance</strong> <strong>and</strong> <strong>Midpoint</strong>.<strong>notebook</strong><br />
August 23, 2012<br />
13 <strong>Distance</strong> <strong>and</strong> <strong>Midpoint</strong>s<br />
segment<br />
two endpoınts <strong>and</strong> all the<br />
poınts between them<br />
A<br />
congruent<br />
two segments that have<br />
the same length<br />
≅<br />
B<br />
congruent<br />
ruler postulate<br />
allows you to measure the length<br />
of any segment<br />
d = |c1-c2|<br />
ab = dıstance of segment ab<br />
ts =<br />
mp =<br />
ms =<br />
m p t s<br />
-5 -4 -3 -2 -1 0 1 2 3 4 5<br />
Aug 138:44 PM<br />
Aug 138:47 PM<br />
clıck<br />
to hear<br />
The distance Formula Song<br />
√(x-x) 2 + (y-y) 2<br />
when fındıng the dıstance<br />
between two poınts,<br />
subtract the two x's<br />
do the same for the y's.<br />
now square both these<br />
numbers,<br />
<strong>and</strong> fınd out theır sum.<br />
when you take the square<br />
root<br />
then you are all done!<br />
example 1<br />
w(1,2)<br />
z(-4,-2)<br />
example 2<br />
p(-3,-5)<br />
q(4,-6)<br />
pull<br />
d = √<br />
Aug 297:41 AM<br />
Aug 139:07 PM<br />
mıdpoınt<br />
the mıdpoınt "m" of pq ıs the poınt<br />
between "p" <strong>and</strong> "q" such that pm = mq .<br />
P M Q<br />
example 3<br />
P M Q<br />
usıng the fıgure above...<br />
pm = 4x + 3<br />
mq = 7x - 6<br />
fınd x.<br />
segment bısector<br />
segment, lıne, or plane that ıntersects<br />
a segment at ıts mıdpoınt.<br />
Aug 232:44 PM<br />
Aug 232:56 PM<br />
1
13 <strong>Distance</strong> <strong>and</strong> <strong>Midpoint</strong>.<strong>notebook</strong><br />
August 23, 2012<br />
example 4<br />
pm = 8x - 5<br />
pq = 28<br />
fınd x.<br />
P M Q<br />
usıng the fıgure above...<br />
<strong>Midpoint</strong> of a Number Line<br />
(<br />
a + b<br />
2<br />
<strong>Midpoint</strong> of Coordinate Plane<br />
x + x , y + y<br />
2 2<br />
(<br />
Aug 232:47 PM<br />
Aug 232:50 PM<br />
starrıng....<br />
mrs. foy<br />
<strong>Midpoint</strong> of Coordinate Plane<br />
(<br />
x + x , y + y<br />
2 2<br />
The <strong>Midpoint</strong> Song<br />
to the tune of "The Itsy Bitsy Spider"<br />
when fındıng the mıdpoınt of two poınts on a<br />
graph,<br />
add the two x's <strong>and</strong> cut theır sum ın half.<br />
add up the y's <strong>and</strong> dıvıde 'em by a two,<br />
now wrıte 'em as an ordered paır<br />
you've got the mıddle of the two.<br />
(<br />
Example 5<br />
fınd the mıdpoınt of fg.<br />
F<br />
0<br />
G<br />
Aug 297:51 AM<br />
Aug 232:52 PM<br />
Example 6<br />
q ıs the mıdpoınt of rs.<br />
r (-3,-4)<br />
s (5,7)<br />
fınd q.<br />
Example 7<br />
n ıs the mıdpoınt of st.<br />
n (4,-1)<br />
s (3,-2)<br />
fınd t.<br />
Aug 232:55 PM<br />
Aug 232:58 PM<br />
2
13 <strong>Distance</strong> <strong>and</strong> <strong>Midpoint</strong>.<strong>notebook</strong><br />
August 23, 2012<br />
Example 8<br />
wy bısects uv at "y" <strong>and</strong><br />
tw bısects uy at "x".<br />
uy = 4x - 3<br />
yv = x<br />
fınd uv.<br />
T<br />
X<br />
Y<br />
V<br />
Example 9<br />
uv = x + 6<br />
uy = x - 1<br />
fınd yv.<br />
T<br />
(<br />
U<br />
X<br />
( (<br />
(<br />
Y<br />
V<br />
W<br />
U<br />
W<br />
Aug 232:59 PM<br />
Aug 233:06 PM<br />
Construction: Bisecting a Segment<br />
draw a segment xy.<br />
x<br />
y<br />
place the compass on "x" <strong>and</strong> measure<br />
greater than half of the segment.<br />
draw arcs above <strong>and</strong> below xy.<br />
do the same for "y". label poınts "p" <strong>and</strong> "q".<br />
connect pq.<br />
X<br />
))<br />
Q<br />
Y<br />
P<br />
))<br />
Aug 233:13 PM<br />
Aug 236:37 PM<br />
3
Attachments<br />
jared fricks.wav<br />
ms bodiford.wav<br />
oldsmoky.mid
Change language