ERIC Number: EJ859252
Record Type: Journal
Publication Date: 2008
Abstractor: As Provided
Reference Count: 0
Collinear Points Problem
Shultz, Harris S.; Shiflett, Ray C.
AMATYC Review, v30 n1 p62-65 Fall 2008
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.
Descriptors: Equations (Mathematics), Algebra, College Mathematics, Two Year Colleges, Mathematical Concepts, Mathematics Instruction, Generalization
American Mathematical Association of Two-Year Colleges. 5983 Macon Cove, Memphis, TN 38134. Tel: 901-333-4643; Fax: 901-333-4651; e-mail: email@example.com; Web site: http://www.amatyc.org
Publication Type: Journal Articles; Reports - Descriptive
Education Level: Two Year Colleges
Authoring Institution: N/A