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identify all the Rays shown in the image below and just as a reminder what array is array starts at some point and then goes on forever in some direction in order to define array you need that point that you're starting off on so let's say that point right over there is called X and then you need another point that sits on the Ray but the Ray is just going to go keep going past it so let's say that that is y over here then we would label this ray we would call it ray X not X X we would rate we would label it X Y and this it says it starts at X so it's starting at X and it keeps on going forever in the direction of Y goes towards Y and then passes Y and then just keeps on going and you need the second point and you need the second point essentially to specify the direction we're going starting an X in the direction of Y going meeting Y then going beyond Y so with that out of the way let's identify all the rays shown in the image below so we can start well we can start really anywhere over here well let's start over here at point J point J we have no array the only Ray that we have or any only line that's really we have or line segment from J is going straight up towards H and then it goes towards HSN it keeps on going so this right over here looks like array and it would be Ray J H Ray J H we're starting at J going through H and then we just keep on going forever now if you go to point H there is no Ray H J because the line ends at J doesn't keep on going forever so there is no Ray H J and there is no Ray H because just with one point you're not specifying array you're not specifying the direction you might be tempted to say that this is a Ray but there's no point over here to help specify the direction so just using this one point you can't say that this ray is starting right over there so looking at this part of our diagram right over here the only Ray the only ray is J H now let's look at the other points so that is J H if we look at Point C once again you might want to create a ray that goes here to the right but there's no other point to specify the direction so we're gonna have to go in the other direction so you could have a ray called C e starts at C goes through E and keeps on going forever so that would be Ray C E and you might say well and you could also have a ray that starts at C goes in the direction of F and goes on forever but these are actually the same Ray these are actually the same Ray because F sits on Ray C E and E sits on Ray CF remember the second point is really just helping you specify the direction that you're going to keep on going in forever so these two are the same race EE is this ray that starts C and keeps on going to the left forever CF is the Ray that starts at C and keeps on going to the left forever so these two are the same ray so they'll only count is one ray now let's go let's think about what we can do from point E well we can start at Point E and keep on and going the direction of C go through C and keep going so that's array you have ray e C you could start at Point E and go in the direction of a and keep going so that's another ray ray e a and you can start at Point E and go in the direction of F and keep going so that is Ray that is Ray EF and just to be clear EF is different than CF because they're starting at two different places they go in the same direction they both go through F but one is starting here and one is starting right over there so that's why those are different Ray's now let's go to I'll pick doing an orange let's think about what we can do from point F point F you might be tempted to go to the left but there's no other point here they haven't given us any other point to specify this direction so let's think about them to the right we could have Ray Fe started F go through E and keep on going so you could have Ray fe2 might say well there's also ray FC started F go through go in the direction of C go through C and keep on going but that's the same thing as f e as f e Point C is on Ray Fe this is Ray Fe right over here and E is on point on ray FC so these are actually the ray and then finally we haven't looked we haven't focused on a point a just yet but you if we go you might say hey maybe there's ray a II but we see the line actually doesn't keep on going on and on forever so that's not a ray and you can't go keep on going to the top right because there's no other point here to specify the direction and so that's about all we can do about finding the Rays given the points that have been specified if they specified some more points for example if they gave us a point right over there we would have been able to define other rays we could have had this you know if this was point G you could have Ray gh you could have had array GE you could have had ray GF but they didn't give us that point and if you had other points over here and here and here you could have had those Ray's that started F to the left H and H going upwards a going to the top right but I didn't specify it so I'm guessing that the way the question was written they say identify all the Rays that have that that involve the blue points that were given in the problem and if we think about those there are 1 2 3 4 5 6 using those original blue points that they gave us in the problem and only those original blue points