in this video we're going to talk about points lines and planes as well as collinear points and coplanar points so a point is just a point in space it's basically a dot a segment connects two points so let's call this point a and point b so this is a segment a 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 no end so array has one arrow so you can write this as ray a b 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 four 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 coplanar 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 always 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 a 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 r 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 nautical planar 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 m but line k 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 actually 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 coplanar points are the points line on plane 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 combined these seven are non-complainant points these five will call planar but once you add e to the mix or f to the mix then they're considered nautical planar points because these points are not all on the same plane so make sure you understand that so these five are coplanar points these six are not complaining points because e is not on 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 e f 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 e f to the mix then it's considered to be non-complaint 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 dc however segment ef is non-coplanar with a b and dc so you can have coplanar segments and nautical planar segments so i'm going to give you some verbal questions regarding these two planes so let me 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 three points determine plane x now what about let's say points f d and r 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 but not x so these three points determine plane y so as we could see it takes at least three non-cooling points to determine a plane now we can also determine a plane using two lines so line ed and lined ac determine which plane so e d 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 e d and line fg these two lines determine which plane so as we said before e d is found in both planes but f g is found in plane y and not x so these two lines determine plane y now here's a question for you point a lies on which plane determine the planes that each of these points lie on a d m f and so forth and r so r is found in plane y f is also in plane y m is found in plane x a is in x and d is at 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 ed is found at the intersection of these two planes so the answer for this is line e d now line e d and point a determine what plane so ed and point a they're both on plane x so determines plane x remember if you have a line and a point they determine only one plane now what about line e d and let's say point f f and e d are found in 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 complaining with these four points are the other points that are 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 they're called planar to plane x now which points oh by the way the other points are non-coplanar 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 b and g they determine plane y so the points that are coplanar to these three points are the other points found in play y so e d r and s are found in plane y 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 a c m and n are not in plane y so therefore these points are non-coplanar to fb and g you