Parallel and Perpendicular Lines

Parallel lines are always the same distance apart from each other and therefore, do not intersect. In Cartesian plane, two lines are parallel if their gradients are equal.
If line L1 is parallel to another line L2 then their slopes will be equal. For example, if the slope of L1 is ‘m’ then the slope of L2 would also be ‘m’.
Perpendicular lines intersect each other at a 90-degree angle. In Cartesian plane, two lines are perpendicular if the product of their gradients is -1.
If line L1 is perpendicular to another line L2 then the slope of L1 will be the negative reciprocal of the slope of L2. For example, if the slope of L1 is ‘m’ then the slope of L2 would be ‘-1/m’.
To check if lines are parallel or perpendicular, first find the equation of each line. This will typically be in the format of y = mx + c where ‘m’ is the gradient and ‘c’ is the y-intercept.
The gradient or slope of a line in a Cartesian plane can be calculated by the change in ‘y’ coordinates divided by the change in ‘x’ coordinates, represented as (y2 - y1)/(x2 - x1).
The y-intercept of a line is the point at which the line crosses the y-axis. In the equation y = mx + c, ‘c’ represents the y-intercept.
Once the equations of two lines have been found, compare the gradients to determine if they are parallel (equal gradients) or perpendicular (product of gradients is -1).
Practice problems to gain a deeper understanding, sketching parallel and perpendicular lines based on their equations and identifying parallel and perpendicular lines in a given diagram on the coordinate plane.
This understanding not only allows for identification and verification of these types of line relationships but also forms a foundational understanding for more complex Calculus topics.