parallel lines, gradient, collinearity
In the applet below, lines f and g are parallel lines.
Interact with this applet by dragging points A, B and C.
Parallel Lines and their Gradients
In general, for two lines and with gradients and respectively,
is parallel to
Collinear Points
If three points are on the same line, they are called collinear points.
Try to make a collinear scenario out of A, B, and C in the above applet.
You will notice that the gradient of AB = gradient of AC = gradient of BC, or