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

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- anonymous

##### 1 Attachment

- anonymous

@jim_thompson5910 can u pleasse help me with a few questions?

- anonymous

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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## More answers

- anonymous

uhhh...

- jim_thompson5910

the points are evenly spaced, so L is the same distance away from both points B and E

- jim_thompson5910

So L is the midpoint of BE

- jim_thompson5910

do you see this?

- anonymous

yea

- jim_thompson5910

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

- jim_thompson5910

what does that give you?

- anonymous

17

- jim_thompson5910

perfect

- anonymous

sweet

- anonymous

can we do number 4 please?

- jim_thompson5910

what is the distance from point T to point E

- anonymous

15

- jim_thompson5910

good, now what's 2/3 of 15?

- anonymous

10

- jim_thompson5910

so the distance from point T to point P is 10 units (since P is 2/3 of the way from T to E)

- jim_thompson5910

So just add 10 to the value of T to get your answer

- anonymous

-4

- jim_thompson5910

good

- anonymous

thanks, im going to post more, maybe u can help me?

- jim_thompson5910

alright go for it

- anonymous

##### 1 Attachment

- jim_thompson5910

tell me what you get for each

- anonymous

1) true
2) True
3) true
4) true
5) False

- jim_thompson5910

did you mean #5 through #9?

- jim_thompson5910

and not #1 through #5

- anonymous

yea

- jim_thompson5910

how did you get #3 to be true?

- anonymous

cause the line goes through the AM

- jim_thompson5910

does it? take a very close look at it

- jim_thompson5910

try to rotate it in your mind

- jim_thompson5910

better yet, get a piece of paper, label it and try it out

- anonymous

k

- anonymous

ohhhhhh i see its like putting a pencil through a peice of paper

- jim_thompson5910

exactly, so do they intersect?

- anonymous

no

- anonymous

are the rest correct?

- jim_thompson5910

good

- jim_thompson5910

why is the last one false?

- anonymous

idk, i wanted to put true, but something was teling me to put false

- jim_thompson5910

do E, D and C all lie on the same line?

- anonymous

yes

- jim_thompson5910

so they are collinear by the very definition of collinear

- jim_thompson5910

points are collinear if they all lie on the same straight line

- jim_thompson5910

Example
|dw:1343852694256:dw|

- jim_thompson5910

Example of non-collinear points
|dw:1343852731003:dw|

- jim_thompson5910

Notice how there is no way to draw a straight line through all of the points, so those points are noncollinear

- anonymous

ohhh

- jim_thompson5910

make sense?

- anonymous

ya

- jim_thompson5910

ok great

- anonymous

##### 1 Attachment

- jim_thompson5910

again tell me what you get

- anonymous

p?

- jim_thompson5910

for #12 right?

- anonymous

ya

- jim_thompson5910

yes, P is coplanar with T, R and Q

- jim_thompson5910

they all lie in the same plane (the back face)

- anonymous

13) rt?

- jim_thompson5910

no, what do the back face and the bottom face have in common (where do they intersect)?

- anonymous

pt?

- jim_thompson5910

you got it

- jim_thompson5910

that bottom edge in the back is what they have in common

- anonymous

##### 1 Attachment

- anonymous

#14) 5?

- jim_thompson5910

#14
how many faces does the figure have?

- anonymous

2?

- anonymous

3

- jim_thompson5910

think of a house

- jim_thompson5910

how many walls does it have?

- anonymous

its the sides u can see right?

- jim_thompson5910

and the sides that are hidden (because they are in the back)

- jim_thompson5910

think of it rotating

- anonymous

4

- jim_thompson5910

4 walls, good

- jim_thompson5910

how many parts to the roof?

- jim_thompson5910

flat parts

- anonymous

6

- jim_thompson5910

6 flat parts to the roof? or 6 total so far?

- anonymous

total

- jim_thompson5910

ok, then count in the floor

- anonymous

7

- anonymous

7

- jim_thompson5910

yes

- jim_thompson5910

there are 7 faces total

- jim_thompson5910

so there are 7 planes

- anonymous

oh ok

- jim_thompson5910

with any geometric solid, a "face" is also a plane

- anonymous

I

- jim_thompson5910

?

- anonymous

number 15 is i ?

- jim_thompson5910

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)

- anonymous

f?

- jim_thompson5910

what also lies on that left wall?

- anonymous

a,d,g,j,f,i

- jim_thompson5910

i and f don't because they lie on the left rooftop

- anonymous

g

- jim_thompson5910

yes, the answer to #15 is g

- anonymous

now for number 16 im confused

- jim_thompson5910

draw a line from D to J

- jim_thompson5910

which face does this line lie in?

- anonymous

jadg

- jim_thompson5910

good

- jim_thompson5910

another way to name JADG is JAD since 3 points are enough to make a plane

- anonymous

is 17 plane JIG?

- anonymous

i mean JGF

- jim_thompson5910

yes, JIG is the same plane as JGF and they both work

- jim_thompson5910

but JGF is the only listed answer, so it's JGF

- anonymous

number 18 "No answer is correct."?

- jim_thompson5910

very good

- jim_thompson5910

there is no face that has the line

- anonymous

sweet!

- anonymous

##### 1 Attachment

- anonymous

non-coplanar ( number 19)

- jim_thompson5910

are you sure? look again (very closely)

- anonymous

collinear

- jim_thompson5910

do they all lie on the same line?

- anonymous

no
non-collinear

- jim_thompson5910

good, so #19 is non-collinear

- anonymous

#20 non-coplanar

- jim_thompson5910

yes, very good

- jim_thompson5910

not all of those 3 points lie in the same plane/face

- anonymous

21 - non-coplanar?

- jim_thompson5910

good, from 20, A, B and G are noncoplanar, so throwing in another point (whatever that new point may be) will not change this

- anonymous

22 - They donâ€™t intersect.

- jim_thompson5910

good

- anonymous

23 - collinear

- jim_thompson5910

do they all lie on the same line?

- anonymous

no
non-coplanar

- jim_thompson5910

so they do NOT lie in the same plane?

- anonymous

no

- jim_thompson5910

are you sure?

- anonymous

yes

- jim_thompson5910

look again

- anonymous

yes they do, coplanar

- jim_thompson5910

yes you are correct

- anonymous

24- collinear

- jim_thompson5910

they all lie on the same line?

- anonymous

yes

- jim_thompson5910

look again

- anonymous

no

- jim_thompson5910

so not colllinear

- jim_thompson5910

collinear*

- anonymous

non-collinear

- jim_thompson5910

good

- anonymous

last one

##### 1 Attachment

- anonymous

non-coplanar

- jim_thompson5910

correct

- anonymous

AWESOME , THANK YOU SO MUCH FOR TAKING TIME TO HELP ME OUT

- jim_thompson5910

you're very welcome

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