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Points, Lines, Planes, Segments, & Rays - Collinear vs Coplanar Points - Geometry



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in this video we're gonna talk about

points lines and planes as well as

collinear points and coplanar points so

a point is just a point in space is

basically a dot a segment connects two

points so let's call this point a and

point B so this is a segment the segment

has a beginning and it has an end so you

can write this as segment a B now array

on the other hand has a beginning but

has a no end so array has one error so

you can write this as array a be a line

has no beginning and no end so you can

write this as line a B with two arrows

now segments Rays and lines they're one

dimensional a horizontal line you can

travel to the right or to the left so

you can only travel in the X direction

for horizontal line now a plane is

two-dimensional you could travel in the

X direction or you could travel in the Y

direction so a plane is flat as a

pancake and like a line it extends

infinitely into the x and y directions

now what is the difference between

collinear points and non collinear

points so let's call this point a B and

C three points are collinear if they lie

on the same line so these are known as

collinear points

now the other three these points are non

collinear because we cannot draw one

line that connects all of them we can

draw a line between two points so we can

say a B is collinear but a b and c are

not collinear because we can't put those

three points in a single line so these

are known as non collinear points

now let's say if we have four points

that lie on the same plane let's call

this point a b c and d these four points

are known as called planar points

because they share the same plane and

let's call this plane x

let's say this is a B C D so these four

points are known as non coplanar points

because they do not lie on the same

plane a B and C lie on the plane but D

is outside of the plane so if we call

this plane M we could say a B and C are

located on plane M but D is not on plane

M so those are non coplanar points now

there's four ways to determine the

existence of a plane the first method is

three non collinear points

there's only is exactly one plane that

can pass through three non collinear

points so that's the first method the

second method is a line and a point only

one plane can pass through a line and a

point so let's call this line m and

point 8 the third method is two parallel

lines let's call this line L and line K

only one plane can pass through two

parallel lines and so these two lines

are known as coplanar lines because they

lie on the same plane now two lines that

intersect also lie on one plane so let's

call this line our and line s they

intersect at this point and so these two

are coplanar lines they share the same

plane

now you can also have non coplanar lines

for example let's say this is line L and

let's say if we have a line

perpendicular to it let's call this line

K so line L lies on plane em but line

kate is not so these are known as non

coplanar lines

now let's say if we have plane Y and

then we have these points

let's call it points a I just want to

make this a b c d let's say this is e f

and g so which of these points are

coplanar points the co-planner points

are the points line on plane and y so a

b c d and g are coplanar points these

five the non coplanar points would be

these five along with e or along with f

so combine these seven are non coplanar

points these five will call planar but

once you add e to the mix or f to the

mix then they're considered non coplanar

points because these points are not all

on the same plane so make sure you

understand that so these five article

planta points these six are NACA planar

points because e is not one plane y and

these seven points are also non coplanar

points now identify the coplanar lines

in this example so we could say that

line CD and line a B are coplanar lines

because they exist on the same plane

now if we add let me draw that better

let's say line EF to the mix then these

three are non coplanar lines a B and D C

are coplanar lines they exist on plane Y

but all three of these once you add EF

to the mix then it's considered to be

nautical plane lines they don't share

the same plane

now what about coplanar segments well

the answer will be the same as coplanar

lines so segment a B which starts here

and ends here is coplanar with segment D

C however segment EF is non coplanar

with a b and d c so you can have

coplanar segments and non coplanar

segments so i'm going to give you some

verbal questions regarding these two

planes so I'm gonna give you three

points points e D and C determine which

of the two planes plane X or plane Y now

notice that point D E and C they're all

located within plane X so these two B

points determine plane X now what about

let's say points F D and are these three

non collinear points determine which

plane so f is on plane Y not X D is on

plane x and y and r is on Y of an X so

these two B points determine plane Y

so as we could see it takes at least

three non Kalina points to determine a

plane now we can also determine a plane

using two lines so line IDI and lined AC

determine which plane so IDI is it's in

both planes x and y but AC is in plane X

and not plane Y so these two lines are

found in plane X so X is the answer for

this example

now what about line IDI and line FG

these two lines determine which plane so

as we said before

Eadie's found in both planes but FG is

found in plane y and not X so these two

lines determine plane Y there's a

question for you

point a lies on which plane the termina

planes that each of these points lie on

a d m f

so R is found and plane Y F is also and

plane Y M is found in plane X a is in X

and D is that the intersection of x and

y so we can write x and y for D

now what is the intersection of x and y

so the intersection between plane x and

plane y is a line and notice that line

Edie is found at the intersection of

these two planes so the answer for this

is line Edie

now line Edie and point a determine what

plane so Edie and point a that will find

a plane X so determines plane X remember

if you have a line and a point they

determine only one plane

now what about line Edie and let's say

point F F and Edie are found and plane Y

so this line in that point determines

plane Y now which points are coplanar

with a b c and d so a b c and d are

found in plane x so the other points

that are complaint with these four

points are the other point that is found

in plane X so E is in plane X G is not M

and n are in plane X G is actually in

plane y is going down so let me just

mark this off so the answer would be e m

and n there coplanar it's a plane X now

which points oh by the way the other

points are nautical planar to it so like

F G R and s are non coplanar to a B C

and D now which points are coplanar to f

b and g so f BN g they determine plane y

so the points that are called planar to

these three points are the other points

found in play y so ii d r and s are

found

in plane why so now which points are non

complainer to FB and G so which points

are found in plane X but not in plane Y

so a c m and n are non complainer to f b

and g these three points they identify

plane y and AC m and n are not in plane

wise so therefore these points are non

coplanar to f BN g