Collinear Lines and Gradients
Collinear points all lie on the same straight line, and proving this is simpler than you might think. When points are collinear, all the line segments between them have identical gradients - that's your key to solving these problems.
To prove collinearity, calculate the gradients between different pairs of points using . If they're equal, state that the segments are parallel and identify the common point they share.
Here's a handy tip: positive gradients slope upwards (like climbing a hill), whilst negative gradients slope downwards. The gradient actually equals tan θ, where θ is the angle between the line and the x-axis.
Quick Check: For negative slopes, find the angle using tan⁻¹, then subtract from 180° to get the actual angle with the x-axis.
