Pairs of lines can be parallel to one another or perpendicular (at right angles).

Points can be collinear, which means they lie on the same line.

Parallel Lines

Lines are parallel if their gradients are the same.

If Line 1 (gradient m1) is parallel to Line 2 (gradient m2) then:

m1 = m2

See example.

Perpendicular Lines

Lines are perpendicular if the product of their gradients is -1

If Line 1 (gradient m1) is perpendicular to Line 2 (gradient m2) then:

m1 x m2 = -1

OR the gradient of one of the lines is the negative reciprocal of the other line's gradient:


See example.

Collinear Points

Collinear points lie on the same line.

To decide whether three points are collinear:

Step 1 Find the gradient of the line joining a pair of the points

Step 2 Find the gradient of the line joining another pair of points.

Step 3 If the gradients are the same and because there is a shared point the points must be collinear.

See example.