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Challenge problem - Given a sheet of paper with two points and their coordinates, how can you find the axes?
You have a sheet of paper with two points and the x and y coordinates are specified for the two points. Assume that the x and y coordinates have the same scale, that is, the distance between, for example, (0,0) and (1,0) is the same as the distance between (0,0) and (0,1). You are given a ruler (not just a straightedge) and a compass. How can you draw the x and y axes? Note that in the most general case of this problem, the axes need not be perpendicular. If you find that confusing, you may assume that the problem has been set up so that the axes are in fact perpendicular. The method of solution is the same in either case.
Things I should have said:
The piece of paper is circular, so there is no way of determining the direction of the axes. Assume that the coordinates of 3 points are given. I realized that there might be more than one possibility with two points. Ignore what I said about the axes not necessarily being perpendicular. Assume that they are in fact perpendicular.
Final Comment:
The question is easier than I first thought. Two points suffice. I am going to add the condition that both the x and y coordinates of the points are different.
1 Answer
- NoneLv 79 years agoFavorite Answer
With perpendicular axes, you need only a ruler and the coordinates of one point to draw the axes. Let the point coordinates be x, y. Select an increment of length on your ruler, measure x units of length horizontally away from the point and draw a vertical line at that distance either to the left or to the right of the point. If the x value is positive, the line will be to the left of the point and vice versa. This line is the y axis. Now measure y units of length either above or below the point (depending on whether y is positive or negative) and draw a horizontal line. This line is the x axis.
