부산대학교 도서관

Students were asked to find all possible values for A so that the points (1, 2), (5, A), and (A, 7) lie on a straight line. This problem suggests a generalization: Given (x, y), find all values of A so that the points (x, y), (5, A), and (A, 7) lie on a straight line. We find that this question about linear equations must be resolved using the more advanced tools of quadratic equations. The number of possible values of A can be zero, one or two, depending upon the given point (x, y). Moreover, the three cases are partitioned by an oblique parabola having its axis at an angle of 45 degrees to the Cartesian plane coordinate axes.