Objectives
The purpose of this activity is to give students an incredibly rich context to calculate and connect midpoints, gradients, perpendicular gradients, equations to lines, simultaneous equations and distance between two points. 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
- Midpoint
- Distance
- Equation (point and gradient)
- Simultaneous Equations
About the Lesson
Students construct a triangle on the Cartesian plane then calculate the gradient of each side, perpendicular gradients and midpoints. This information is used to determine equations to the perpendicular bisectors (gradient and point). The equations all intersect at one point (circumcentre) which students confirm using simultaneous equations. Finally students check the distance to each vertex and determine the equation to a circle (circumcircle) that passes through each vertex. Extension material is included in this activity.