Activity Overview
This activity is part of the coordinate geometry series. In this activity students use the midpoint tool to explore and establish the formula for the midpoint of two points. Students then go on to explore the path of the midpoint for a fixed point and a point on a line.
Objectives
The aim of this investigation is for students to establish a formula for the coordinates of a midpoint through exploration. Students are then able to take their model and apply it to more challenging problems such as the set of midpoints between a fixed point A and a point on a line.
Vocabulary
- Midpoint
- Abscissa
- Ordinate
- Locus
About the Lesson
Students create two points on the Cartesian plane and then use the geometry tools to construct a midpoint. Students move their points around to specific locations and track the coordinates of the midpoint with a view to establishing a formula. Students test and practice using their midpoint formula and then extend to the path of a midpoint between a stationary point and a point on a line, including a quadratic function.