Activity Overview
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Coordinate Geometry - Students calculate midpoints, gradients, perpendicular lines and use simultaneous equations to help determine the location of the orthocentre. A really cool property of the orthocentre is revealed in the extension component of the activity.
Objectives
The purpose of this activity is to give students an incredibly rich context to calculate and connect gradients, perpendicular gradients, equations to lines and simultaneous equations. Students jump from one calculation to another rather than repeating a single calculation type (without context). At the same time there is a wealth of beautiful geometry in this activity and the remaining activities in this series.
Vocabulary
- Gradient
- Perpendicular
- Linear Equation
- Simultaneous Equations
- Reflection
About the Lesson
Students construct a triangle on the Cartesian plane, calculate the gradient of each side and the perpendicular gradients. This information is used to determine equations to the altitudes (gradient and point). The equations all intersect at one point (orthocentre) which students confirm using simultaneous equations. Extension material is included in this activity that shows a remarkable connection between the orthocentre and the circumcentre of a triangle.