Slopes and Circles

The purpose of this task is to lead students through an algebraic approach to a well-known result from classical geometry, namely, that a point X is on the circle of diameter AB whenever angle AXB is a right angle.
Resource ID#: 44538 Type: Problem-Solving Task
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General Information

Subject(s): Mathematics
Grade Level(s): 9, 10, 11, 12
Intended Audience: Educators educators, Students , Parents
Suggested Technology: Adobe Acrobat Reader, Microsoft Office
Instructional Time: 15 Minute(s)
Keywords: slope, right angle, perpendicular lines, algebraic manipulations, Thales' Theorem, Florida Standards, pythagorean theorem, right triangles, application, real world, distance, diameter, radius, circle, slope, slope formula, positive slope, negative slope, slope formula (y2-y1)/(x2-x1) = m, coordinates, coordinate grid, mathematics, interactive, tutorials, product of slopes is -1, cpalms, icpalms, illustrativemathematics.org, illustrative mathematics, tasks, mathematics, math, Florida standards, resource, free, freely available, problems-based learning, student activities
Instructional Component Type(s): Problem-Solving Task
Resource Collection: Illustrative Mathematics

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