Know the Relationship between the Gradients of Parallel and Perpendicular Lines

Understanding the relationship between the gradients of parallel and perpendicular lines is essential for solving problems in coordinate geometry. This understanding can help you identify whether given lines are parallel, perpendicular or neither.

Parallel Lines

Two lines are parallel if and only if their gradients are equal.
- For example, if line A has a gradient of 3, and line B also has a gradient of 3, lines A and B are parallel.
- Symbolic representation: If line 1 has gradient m1 and line 2 has gradient m2, then m1 = m2.

Perpendicular lines

Two lines are perpendicular to each other if and only if the product of their gradients is -1. This means that the gradient of one line is the negative reciprocal of the gradient of the other line.
- For example, if line A has a gradient of 2, and line B has a gradient of -1/2, then lines A and B are perpendicular.
- Symbolic representation: If line 1 has gradient m1 and line 2 has gradient m2 then m1 * m2 = -1.

Remember: If two lines are neither parallel nor perpendicular, there is no special relationship between their gradients. They could intersect at any angle.