*HAPPY THANKSGIVING!*

*Alright, you're teaching about the rule for slopes of perpendicular lines in Algebra or Geometry.*

Here are some of the instructional strategies or approaches you may have used...

(1) State the theorem without explanation followed by 3-4 demo examples of how it's used

(2) Motivate the theorem using the lines

*y = (3/4)x*and

*y = (-4/3)x*, choosing the points (4,3) and (-3,4) to demonstrate why these lines are perpendicular

(3) A more abstract approach using the following diagram

**NOTE**: Q(-b,a) is the point on line M in quadrant II. The label is too far from the dot!

**FROM THE GIVEN INFORMATION IN THE DIAGRAM PROVE THAT ∠QOP IS A RIGHT ANGLE, THAT IS, LINES L AND M ARE PERPENDICULAR.**

**Comments**

**(4,3) and (-6,8)**on the lines? I personally would prefer this (and not give the equations of the lines). What do you imagine most students would do with this problem a few weeks (or even days!) later? Would they make the connection to slopes immediately if they had moved on to another unit or if this appeared on an assessment?

**Exactly what questions would you ask to promote a generalization?***By the way, do you believe it is likely or unlikely that some version of this problem might appear on a standardized test like ADP's Algebra 2 End of Course Test or the SATs?*