Education Technology

Amazing Locus

Activity Overview

Students are presented with a challenging problem and provided with the tools to help break it down to see the relatively simple, yet amazing, solution. The problem requires students to calculate gradients, gradients of perpendicular lines, the equation of a line given point and gradient and finally solve a set of equations simultaneously. 


There are many other coordinate geometry problems that students could tackle, but this one is particularly nice. The wording is enough to stump most students, yet the solution process is relatively straight forward. So this activity aims to help students get started on challenging worded problem by breaking them down, one step at a time.  


  • Triangle
  • Vertices
  • Locus
  • Gradient
  • Perpendicular
  • Simultaneous Equations

About the Lesson

Students are presented with a challenging problem. The teacher notes provide lots of strategies on how to break down the question to help students get started. The activity sheet provides similar scaffolding. Students solve for a specific common solution, students then move on to their own set of points and finally the general solution. The final answer to the question is amazing, providing opportunities to extend this problem to other functions or other triangle centers.