hali12
In the figure below, all the points are evenly spaced along the line. What is the coordinate of point L?



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hali12
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hali12
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@jim_thompson5910 can u pleasse help me with a few questions?

completeidiot
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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

hali12
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uhhh...

jim_thompson5910
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the points are evenly spaced, so L is the same distance away from both points B and E

jim_thompson5910
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So L is the midpoint of BE

jim_thompson5910
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do you see this?

hali12
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yea

jim_thompson5910
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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
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what does that give you?

hali12
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17

jim_thompson5910
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perfect

hali12
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sweet

hali12
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can we do number 4 please?

jim_thompson5910
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what is the distance from point T to point E

hali12
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15

jim_thompson5910
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good, now what's 2/3 of 15?

hali12
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10

jim_thompson5910
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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
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So just add 10 to the value of T to get your answer

hali12
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4


hali12
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thanks, im going to post more, maybe u can help me?

jim_thompson5910
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alright go for it

hali12
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jim_thompson5910
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tell me what you get for each

hali12
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1) true
2) True
3) true
4) true
5) False

jim_thompson5910
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did you mean #5 through #9?

jim_thompson5910
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and not #1 through #5

hali12
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yea

jim_thompson5910
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how did you get #3 to be true?

hali12
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cause the line goes through the AM

jim_thompson5910
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does it? take a very close look at it

jim_thompson5910
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try to rotate it in your mind

jim_thompson5910
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better yet, get a piece of paper, label it and try it out

hali12
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k

hali12
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ohhhhhh i see its like putting a pencil through a peice of paper

jim_thompson5910
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exactly, so do they intersect?

hali12
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no

hali12
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are the rest correct?


jim_thompson5910
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why is the last one false?

hali12
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idk, i wanted to put true, but something was teling me to put false

jim_thompson5910
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do E, D and C all lie on the same line?

hali12
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yes

jim_thompson5910
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so they are collinear by the very definition of collinear

jim_thompson5910
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points are collinear if they all lie on the same straight line

jim_thompson5910
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Example
dw:1343852694256:dw

jim_thompson5910
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Example of noncollinear points
dw:1343852731003:dw

jim_thompson5910
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Notice how there is no way to draw a straight line through all of the points, so those points are noncollinear

hali12
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ohhh

jim_thompson5910
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make sense?

hali12
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ya

jim_thompson5910
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ok great

hali12
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jim_thompson5910
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again tell me what you get

hali12
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p?

jim_thompson5910
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for #12 right?

hali12
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ya

jim_thompson5910
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yes, P is coplanar with T, R and Q

jim_thompson5910
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they all lie in the same plane (the back face)

hali12
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13) rt?

jim_thompson5910
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no, what do the back face and the bottom face have in common (where do they intersect)?

hali12
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pt?

jim_thompson5910
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you got it

jim_thompson5910
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that bottom edge in the back is what they have in common

hali12
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hali12
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#14) 5?

jim_thompson5910
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#14
how many faces does the figure have?

hali12
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2?

hali12
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3

jim_thompson5910
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think of a house

jim_thompson5910
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how many walls does it have?

hali12
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its the sides u can see right?

jim_thompson5910
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and the sides that are hidden (because they are in the back)

jim_thompson5910
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think of it rotating

hali12
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4

jim_thompson5910
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4 walls, good

jim_thompson5910
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how many parts to the roof?

jim_thompson5910
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flat parts

hali12
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6

jim_thompson5910
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6 flat parts to the roof? or 6 total so far?

hali12
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total

jim_thompson5910
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ok, then count in the floor

hali12
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7

hali12
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7


jim_thompson5910
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there are 7 faces total

jim_thompson5910
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so there are 7 planes

hali12
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oh ok

jim_thompson5910
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with any geometric solid, a "face" is also a plane

hali12
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I


hali12
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number 15 is i ?

jim_thompson5910
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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)

hali12
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f?

jim_thompson5910
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what also lies on that left wall?

hali12
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a,d,g,j,f,i

jim_thompson5910
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i and f don't because they lie on the left rooftop

hali12
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g

jim_thompson5910
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yes, the answer to #15 is g

hali12
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now for number 16 im confused

jim_thompson5910
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draw a line from D to J

jim_thompson5910
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which face does this line lie in?

hali12
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jadg


jim_thompson5910
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another way to name JADG is JAD since 3 points are enough to make a plane

hali12
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is 17 plane JIG?

hali12
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i mean JGF

jim_thompson5910
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yes, JIG is the same plane as JGF and they both work

jim_thompson5910
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but JGF is the only listed answer, so it's JGF

hali12
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number 18 "No answer is correct."?

jim_thompson5910
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very good

jim_thompson5910
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there is no face that has the line

hali12
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sweet!

hali12
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hali12
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noncoplanar ( number 19)

jim_thompson5910
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are you sure? look again (very closely)

hali12
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collinear

jim_thompson5910
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do they all lie on the same line?

hali12
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no
noncollinear

jim_thompson5910
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good, so #19 is noncollinear

hali12
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#20 noncoplanar

jim_thompson5910
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yes, very good

jim_thompson5910
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not all of those 3 points lie in the same plane/face

hali12
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21  noncoplanar?

jim_thompson5910
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good, from 20, A, B and G are noncoplanar, so throwing in another point (whatever that new point may be) will not change this

hali12
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22  They don’t intersect.


hali12
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23  collinear

jim_thompson5910
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do they all lie on the same line?

hali12
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no
noncoplanar

jim_thompson5910
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so they do NOT lie in the same plane?

hali12
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no

jim_thompson5910
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are you sure?

hali12
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yes

jim_thompson5910
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look again

hali12
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yes they do, coplanar

jim_thompson5910
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yes you are correct

hali12
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24 collinear

jim_thompson5910
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they all lie on the same line?

hali12
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yes

jim_thompson5910
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look again

hali12
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no

jim_thompson5910
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so not colllinear

jim_thompson5910
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collinear*

hali12
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noncollinear


hali12
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last one

hali12
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noncoplanar

jim_thompson5910
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correct

hali12
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AWESOME , THANK YOU SO MUCH FOR TAKING TIME TO HELP ME OUT

jim_thompson5910
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you're very welcome