Show three points are collinear
A standard method from Coordinates: the steps and worked examples.
Steps
- Find the slope of AB.
- Find the slope of BC.
- If the slopes are equal, AB and BC are parallel and share the point B, so they are one line: A, B and C are collinear.
Worked examples
Example 1: Show that the three points P(−1, −1), Q(1, 3) and R(3, 7) are collinear.
slope PQ = (3 − (−1))/(1 − (−1)) = 4/2 = 2
slope QR = (7 − 3)/(3 − 1) = 4/2 = 2
slope PQ = slope QR and Q is a common point
∴ P, Q and R are collinearFor the whole topic, read Coordinates: key points, common mistakes and how the DSE tests it.