**ERIC Number:**EJ859252

**Record Type:**Journal

**Publication Date:**2008

**Pages:**4

**Abstractor:**As Provided

**Reference Count:**0

**ISBN:**N/A

**ISSN:**ISSN-0740-8404

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: amatyc@amatyc.org; Web site: http://www.amatyc.org

**Publication Type:**Journal Articles; Reports - Descriptive

**Education Level:**Two Year Colleges

**Audience:**N/A

**Language:**English

**Sponsor:**N/A

**Authoring Institution:**N/A