COORDINATE GEOMETRY · SECTION FORMULA · INVESTIGATION 05
Section Formula & Midpoint Lab
Investigate internal division of a line segment in a given ratio and the special case of its midpoint.
Interactive mathematical workspace
Live simulationThe model updates as you adjust the apparatus controls. Values are simulated mathematical outputs, not physical measurements.
Primary result—
Secondary result—
Relationship—
Check—
Adjust a control to begin the investigation.
Learning objective
To investigate Section Formula & Midpoint Lab using a dynamic mathematical model and justify a conclusion from recorded values.
Mathematical principle
P = ((mx₂ + nx₁)/(m+n), (my₂ + ny₁)/(m+n))
Procedure
1
Enter student details and note the initial settings.
2
Change one independent variable while keeping the others fixed.
3
Observe the visual model and note the calculated values.
4
Repeat with at least three different settings and record the readings.
5
Use the pattern in your observations to write a mathematical conclusion.
Variables
Independent: the control being changed. Dependent: calculated result. Controlled: other settings held constant.
Guided investigation: Change m:n and observe how P moves along AB. Set m = n for the midpoint.
Common errors to avoid
- Changing several variables simultaneously.
- Recording rounded values before completing calculations.
- Confusing linear, square and cubic units.
- Writing a conclusion that is not supported by observations.
Live mathematical analysis
P = ((mx₂ + nx₁)/(m+n), (my₂ + ny₁)/(m+n))
The working will appear here.
Observation table
| Trial | Settings | Result 1 | Result 2 |
|---|---|---|---|
| Run and record trials to populate this table. | |||
Compare the readings and identify the pattern.
Digital practical notebook
Recorded trials
| # | Settings | Result 1 | Result 2 | Time |
|---|
Knowledge check
Select the best answer. Feedback is provided after checking.
Assessment score0 / 5
Investigation challenge
Find the midpoint of A(−4,2) and B(6,8).