# Thread: What does the sign of each of the coordinates of a triangle tell you about the plane

1. ## What does the sign of each of the coordinates of a triangle tell you about the plane

Hi, I have the following problem, and I don't know if I got it right because of the last bit between brackets. I will also give my answers at the end. I would really appreciate it if you could give me a hand if I got it wrong... thanks!

"Let ABC be a triangle and consider 'triangle coordinates' x, y, z. Try and understand how these coordinates relate to the triangle: what does it mean for one of them to be zero for a point? What does the sign of the three coordinates tell you about where in the plane the point is? (You might want to reflect on the fact that the lines forming the sides of the triangle, when extended, divide the plane into seven regions.)"

So yeah, for the first question I think it means that it is the origin (0,0). Is that right?

As for the second one, at first I thought it had something to do with the 4 quadrants, that if it is positive it is in the first quadrant, and if it is negative it has to be in the third quadrant...but I don't think that is the right answer because of the extra information given between brackets. :S

2. Originally Posted by jmgilbert
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"Let ABC be a triangle and consider 'triangle coordinates' x, y, z. Try and understand how these coordinates relate to the triangle: what does it mean for one of them to be zero for a point?
According to your question the triangle is in 3D-space.
If one coordinate is zero then the point is located in one of the three coordinate planes. For instance: All points with the coordinates (x, 0, z) are placed in the xz-plane.
If two of the three coordinates are zero then the point is placed on one of the three coordinate axes.
If all three coordinates are zero then the point is the origin.
What does the sign of the three coordinates tell you about where in the plane the point is? (You might want to reflect on the fact that the lines forming the sides of the triangle, when extended, divide the plane into seven regions.)"

So yeah, for the first question I think it means that it is the origin (0,0). Is that right?

As for the second one, at first I thought it had something to do with the 4 quadrants, that if it is positive it is in the first quadrant, and if it is negative it has to be in the third quadrant...but I don't think that is the right answer because of the extra information given between brackets. :S
You are refering to the plane. Which plane?
Or do you want to determine the oktant of the coordinate system by the signs of the coordinates of a certain point?

3. Thanks for your help! I am going to ask my teacher about the second question when I see him around because it should not say "plane". I'll ask him to clarify me the question.