Lines L and M are perpendicular. Line L contains (0,0). Lines L and M intersect at A(5,2). Find x.
(1) Would students in geometry be more likely to consider some or all of the following: similar triangles, altitudes on hypotenuse theorems, areas, Pythagorean approaches? If this were presented as a coordinate problem in Algebra 2, what would be the most likely approach? Would some students use the distance formula?
(2) As always, it is our role as educators to present these kinds of challenges and to encourage students to think more deeply. Making connections between algebra and geometry happens naturally for some, but certainly not for all! We must enable this dialogue via the classroomm environment we establish and the kinds of questions we ask. It is important to first decide the goal. What concepts are we trying to develop? Slope? Ratios of corresponding parts? How many students never make the connection between the two!
(3) The answer is 29/5 or 5.8. Think of at least two methods!