Gradient, distance and midpoint partner activity (Investigation)
Two points, three calculations - a review
Given any two points, we can calculate many different properties of the interval or line segment joining the two points. Such calculations include the gradient between the points, the midpoint of the two points, and the distance between two points. The calculations for these properties are briefly reviewed below or in more detail by clicking the links above.
For two points, A \left(x_1,y_1\right) and B \left(x_2, y_2\right), we can find the gradient of the line segment between them using the formula m=\frac{y_2-y_1}{x_2-x_1}
For two points, A \left(x_1,y_1\right) and B \left(x_2, y_2\right), we can find the midpoint between them using the formula M_{AB}=\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right).
For two points, A \left(x_1,y_1\right) and B \left(x_2, y_2\right), we can find the distance between them using the formula d=\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}.
Partner activity
In this activity, first one partner will set up a question and the other partner will perform the calculations. Points are earned for each correct calculation. Part marks can be awarded to partially correct solutions if desired. The roles are then swapped and repeat until the first person gets to 36 points.
| Calculation | Number of points, if correct |
|---|---|
| Gradient | 1 |
| Midpoint | 2 |
| Distance | 3 |
- Open the GeoGebra applet below
- Partner 1 - Create questions for your partner by clicking and moving the two points.
- Partner 2 - Calculate the gradient, midpoint and distance between the two points chosen by your partner.
- Partner 1 - Check your partner's answers by selecting the checkbox for each value one at a time.
- Partner 2 - For any incorrect calculations, "Show Full Solution" and see if you can find your error. You can step forwards and backwards through the solution using the slider in the bottom left corner.
- Partner 2 - Calculate the number of points you earned that round and record (maximum of 6 points)
- Repeat with partner 1 and 2 swapped around.
To increase the challenge, consider using non-integer values or not showing your partner the diagram and having them just use the coordinates of the points.
Discussion Questions
- Which calculation overall went the best for you, the gradient, midpoint, or distance? Why do you think this was?
- Did you find yourself using the formulas or the conceptual definitions more? Did it depend on the calculation?
- Is it easier or more challenging calculating without the diagram compared to when given the diagram?
- If you are given one point and the gradient, can you determine the other point uniquely? Explain.
- If you are given one point and the midpoint, can you determine the other point uniquely? Explain.
- If you are given one point and the distance, can you determine the other point uniquely? Explain.
- If you are given one point, the gradient and the distance, can you determine the other point uniquely? Explain.