Another Geometry question (easy one this time.) Can you help me?
Asked by
Val123 (
12734
)
June 30th, 2010
Dealing with graphing, the X,Y axis, which creates a quadrant. In one lesson I saw today, they labeled the quadrants clockwise, from top right (I) to bottom right (II) to bottom left (III) to top left (IV). Now, are those quadrant labels ALWAYS labeled in that direction, starting with the top right, or can that change with the whims of whomever built the thing?
I ask because a student was having a hard time graphing something like (5, -3). I pointed out the way they labeled the quadrants in the previous lesson, it seemed it would put it in IV, but the answer was in Q3….
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4 Answers
All the pictures I have seen of graphing quadrants, have labeled the 4 areas in a counterclockwise way. Top right is I & bottom right is IV. Even after doing a quick google search just now on the matter, all the images & print outs of graphing paper have labeled the quadrants in this way. Because math is an exact science, quadrant labeling isn’t about personal preference.
Which text are you using? The exercises and solutions seem to be nonsensical or incorrect. That might explain the difficulties you’re experiencing. As noted above, the quadrants are numbered counterclockwise with the upper right being I.
QI: x positive, y positive.
QII: x negative, y positive.
QIII: x negative, y negative.
QIV: x positive, y negative.
Thus, (5, -3) is in QIV.
See Cartesian Coordinates for more details.
I am used to seeing the quadrants labelled anti-clockwise starting with Xpos,Ypos as quadrant 1 and Xpos,Yneg as quadrant 4. That being said, the labelling is completely arbitrary and can change as whims desire. The labelled quadrants are not an inherent part of the x-y graph.
As for how you knew what the answer is, I assume that you consulted a solutions manuel/teacher’s textbook. I have to confess that 100% of the time that the solutions manuel disagrees with my answer, I chalk it up to a typographical or mathematical error of the solution’s author. I always try to encourage my students to do the same (as long as they’ve double-checked their work); having the confidence to stand behind your logical work towards an answer is one of the major benefits of studying mathematics in my opinion.
Thanks you guys…..I’ll double check it again.
@noodlehead710 I’m the teacher. I have the answer key. I’m teaching HS summer school, ALL courses, and my higher math is really rusty. But I’m getting there.
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