Education Technology

Euler Line

Activity Overview

This activity combines the result of the Circumcentre, Orthocentre and Centroid activities to locate the Euler line. The problem is explored entirely on the Cartesian plane and provides ample opportunity for students to demonstrate an understanding of perpendicular lines and midpoints, determination of equations and solutions to simultaneous equations with a purpose. 


The aim of this activity is to bring the Circumcentre, Orthocentre and Centroid activities together. The activity reviews the previous content and then uses the information to determine an equation for the Euler line in addition to a single formula that determines the gradient of the Euler line using only the gradients of the triangles sides. 


  • Gradient
  • Perpendicular
  • Midpoint
  • Straight line equation
  • Collinear

About the Lesson

Students review their results from the Circumcentre, Centroid and Orthocentre investigations to locate the Euler line and then test a formula that relates the gradient of each side of the triangle to the gradient of the Euler line.