Question

How do I find the intersection of each pair of planes or lines (see attached photo) please

Answer 1

tht hard tbh

Answer 2

im sorry i cannot help u

Answer 3

i can give u answer but not how to do it :)

Answer 4

ikr

Answer 5

people r replying to mine omg ty

Answer 6

@jim_thompson5910 please help

Answer 7

he is good

Answer 8

if two planes intersect, you get a line or line segment

if two lines intersect, then you get a point

Answer 9

@jim_thompson5910 i dont know how to find planes

Answer 10

a plane is just a flat surface

so for instance, the bottom face made up by the points OPQR is one plane
the front face is made up by the points DRQC

they intersect or cross to form the line segment RQ

Answer 11

make sense?

Answer 12

@jim_thompson5910 that makes sense but in my book it says planes " ABP" and "BCD" but wouldnt it be planes "ABPO" and "BCDA" (look @ pic)

Answer 13

you only need 3 points to make a plane

the 4th point is extra and unneccesary

Answer 14

@jim_thompson5910 so the 4th letter should be included but it isnt?

Answer 15

so ABPO is the same as ABP and you don't need that fourth point O

Answer 16

no it doesn't have to be included because it's extra info that you don't need

Answer 17

@jim_thompson5910 but that is part of the planes right

Answer 18

yes but you need a min of 3 points

using that 4th point is just extra work

why go through all that trouble when you can use 3 points

Answer 19

if you can say the same thing, but in a shorter way, then why not go for it

Answer 20

@jim_thompson5910 ok so the intersection of planes ABP and BCD would be would be what idk how to find that

Answer 21

line AD?

Answer 22

plane ABP (aka plane ABPO) is the very back face

plane BCD (aka plane BCDA) is the top face

Answer 23

what do they both have in common? where do they cross or intersect?

Answer 24

line BP?

Answer 25

@jim_thompson5910

Answer 26

one sec, I'm going to post an image

Answer 27

ok

Answer 28

here is the back face ABP or ABPO

Answer 29

here is the top face BCD or BCDA

Answer 30

and here are the two faces highlighted together (red on top, blue in back)

you can see they intersect at line AB

Answer 31

couldnt they also intersect line AD

Answer 32

no AD is part of the top face, but NOT part of the back face

Answer 33

when two planes intersect, they will only have 1 line in common

Answer 34

oh

Answer 35

so lines RQ and RO would intersect where im so confused sorry

Answer 36

well if you ignore the picture, what do RQ and RO have in common (in terms of letters)

Answer 37

oh R

Answer 38

so it would just be Point R? @jim_thompson5910

Answer 39

and the same thing goes for planes ADR and DCQ ?

Answer 40

Or since its DCQR they would have points D and R in common i dont know ughj

Answer 41

OH WAIT so for planes ADR AND DCQ it would be line DR? @jim_thompson5910

Answer 42

RQ and RO have point R in common

good

Answer 43

so RQ and RO intersect at point R

Answer 44

and you're correct again, planes ADR and DCQ intersect at line DR

Answer 45

so do they intersect at point R or line DR @jim_thompson5910 ?

Answer 46

depends on if you're asking about the lines intersecting or the planes intersecting

Answer 47

RQ and RO are two lines that intersect at the point R

ADR and DCQ are two planes that intersect at line DR

Answer 48

ok

Answer 49

wold plane BCQ just be plane BCQ or would it be BCQP

Answer 50

@jim_thompson5910

Answer 51

BCQ is a shorter way to refer to BCQP

I would go with BCQ since it's faster

Answer 52

@jim_thompson5910 i know but is the whole thing BCQP

Answer 53

yes it is

but there's no need to list P since BCQ does the job just fine

Answer 54

ok and the intersectino to planes BCD and BCQ would be point B or

Answer 55

I Mean they share points B,C,and A

Answer 56

point A is part of the top face

but it is NOT part of the face on the right side

Answer 57

so they intersect at line BC

Answer 58

only B and C are in common

so put together, the two planes intersect to form segment BC

Answer 59

good you beat me to it

Answer 60

segment BC or line BC

Answer 61

segment

Answer 62

it doesn't stretch on forever in both directions, so it's not a line

it's a segment

Answer 63

then why did we say line BR for the intersection of the planes ADR and DCQ

Answer 64

we didn't say BR

we said DR

Answer 65

i mean DR

Answer 66

because points D and R are on BOTH planes

Answer 67

any point between D and R are also on both

so overall, segment DR is on both planes

Answer 68

segment??

Answer 69

yes it's a segment

Answer 70

line or segment BC is on both planes too

Answer 71

you just said it was a line tho

Answer 72

ughhj

Answer 73

sorry I mixed up terms

DR is a segment since it's not infinitely long

Answer 74

how do u know if it is infinitely long

Answer 75

example, this is a line because it goes on forever in both directions

Answer 76

this is a line segment or a segment (let's call it a segment only to avoid confusing terms)



since it's not infinitely long

Answer 77

the arrows indicate if the line stretches on forever

Answer 78

@jim_thompson5910 but how can you tell that on a figure? (the pic)

Answer 79

there are no arrows on any of the lines, so they are segments that do NOT go on forever

Answer 80

they are segments with a set and fixed length

Answer 81

@jim_thompson5910 so every 2 points on the figure that connect is a segment and there are no lines

Answer 82

correct, that's a very good way of looking at it

Answer 83

a segment has 2 endpoints

a line does not have any endpoints

Answer 84

so for the one I asked about the planes ABP and BCD they woud intersect at SEGMENT AB not line AB

Answer 85

yes that is correct

Answer 86

the confusing thing about geometry is that the term "line" is used very loosely

but to be very very technical, a line is something that is straight and it extends in both directions forever

a segment is something that has 2 endpoints (technically though, a segment is a line since you can call it a line segment...just stick with "segment" though)

Answer 87

@jim_thompson5910 so in all of geometry whenever there is figure and they ask you to name the intersection of each pair planes or lines on a figure its always gonna be a point or a segment? right?