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In the figure below, all the points are evenly spaced along the line. What is the coordinate of point L?

Mathematics
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1 Attachment
@jim_thompson5910 can u pleasse help me with a few questions?
8+x=L L+x=26 substitute (8+x)+x=26 x is the same for both expressions because the points are equally spaced solve for x, then solve for L

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Other answers:

uhhh...
the points are evenly spaced, so L is the same distance away from both points B and E
So L is the midpoint of BE
do you see this?
yea
so we can say (B+E)/2 = L or basically take the value of B, add it to E, then divide by 2 to get L
what does that give you?
17
perfect
sweet
can we do number 4 please?
what is the distance from point T to point E
15
good, now what's 2/3 of 15?
10
so the distance from point T to point P is 10 units (since P is 2/3 of the way from T to E)
So just add 10 to the value of T to get your answer
-4
good
thanks, im going to post more, maybe u can help me?
alright go for it
1 Attachment
tell me what you get for each
1) true 2) True 3) true 4) true 5) False
did you mean #5 through #9?
and not #1 through #5
yea
how did you get #3 to be true?
cause the line goes through the AM
does it? take a very close look at it
try to rotate it in your mind
better yet, get a piece of paper, label it and try it out
k
ohhhhhh i see its like putting a pencil through a peice of paper
exactly, so do they intersect?
no
are the rest correct?
good
why is the last one false?
idk, i wanted to put true, but something was teling me to put false
do E, D and C all lie on the same line?
yes
so they are collinear by the very definition of collinear
points are collinear if they all lie on the same straight line
Example |dw:1343852694256:dw|
Example of non-collinear points |dw:1343852731003:dw|
Notice how there is no way to draw a straight line through all of the points, so those points are noncollinear
ohhh
make sense?
ya
ok great
1 Attachment
again tell me what you get
p?
for #12 right?
ya
yes, P is coplanar with T, R and Q
they all lie in the same plane (the back face)
13) rt?
no, what do the back face and the bottom face have in common (where do they intersect)?
pt?
you got it
that bottom edge in the back is what they have in common
1 Attachment
#14) 5?
#14 how many faces does the figure have?
2?
3
think of a house
how many walls does it have?
its the sides u can see right?
and the sides that are hidden (because they are in the back)
think of it rotating
4
4 walls, good
how many parts to the roof?
flat parts
6
6 flat parts to the roof? or 6 total so far?
total
ok, then count in the floor
7
7
yes
there are 7 faces total
so there are 7 planes
oh ok
with any geometric solid, a "face" is also a plane
I
?
number 15 is i ?
points D, J and A all lie on the left wall (that's behind the front and right walls...so it's hidden from view)
f?
what also lies on that left wall?
a,d,g,j,f,i
i and f don't because they lie on the left rooftop
g
yes, the answer to #15 is g
now for number 16 im confused
draw a line from D to J
which face does this line lie in?
jadg
good
another way to name JADG is JAD since 3 points are enough to make a plane
is 17 plane JIG?
i mean JGF
yes, JIG is the same plane as JGF and they both work
but JGF is the only listed answer, so it's JGF
number 18 "No answer is correct."?
very good
there is no face that has the line
sweet!
1 Attachment
non-coplanar ( number 19)
are you sure? look again (very closely)
collinear
do they all lie on the same line?
no non-collinear
good, so #19 is non-collinear
#20 non-coplanar
yes, very good
not all of those 3 points lie in the same plane/face
21 - non-coplanar?
good, from 20, A, B and G are noncoplanar, so throwing in another point (whatever that new point may be) will not change this
22 - They don’t intersect.
good
23 - collinear
do they all lie on the same line?
no non-coplanar
so they do NOT lie in the same plane?
no
are you sure?
yes
look again
yes they do, coplanar
yes you are correct
24- collinear
they all lie on the same line?
yes
look again
no
so not colllinear
collinear*
non-collinear
good
last one
1 Attachment
non-coplanar
correct
AWESOME , THANK YOU SO MUCH FOR TAKING TIME TO HELP ME OUT
you're very welcome

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