Question

How do you determine if a line is perpendicular, parallel, or neither?

Answer 1

We have different types and different kinds of lines. We can also determine the line by using some methods. By using the slope of a linear function and some characteristics of line you can distinguish the given line is a parallel, perpendicular or neither

Complete step by step explanation:
To determine if a line is perpendicular, parallel, or neither first find the slope of the line. The slope of a line characterizes the direction of a line. To find the slope, you divide the difference of the y-
coordinates of 2 points on a line by the difference of the x-coordinates of those same 2 points
i.e., $slope = \dfrac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}$

Parallel lines : The characteristic of parallel lines are If a set of parallel lines in a plane that will never intersect means lines will continue on forever without ever touching. A set of parallel lines having the identical or same slope. Parallel lines are most commonly represented by two vertical lines $\left( {||} \right)$. For example the line AB parallel to line CD represented as $AB||CD$.

Example : A square, Rectangle and parallelogram consists of four sides. Each side is parallel to
its opposite side.

Perpendicular lines : The characteristic of perpendicular lines are If a perpendicular lines cross to form ${90^ \circ }$ angles at the intersection line. The slope of perpendicular lines are negative reciprocals means the product of the slopes of perpendicular lines is equal to -1. Perpendicular lines are most commonly represented as $\left( \bot \right)$. For example the line AB perpendicular to line CD represented as $AB \bot CD$.

Example : The walls meeting floors and ceilings.

Characteristics of Lines that are Neither Parallel nor Perpendicular is that slopes of lines are not the same and the lines are intersect although they do not form ${90^ \circ }$ angles.

Example : The hour and minute hands of clock at 4:30 p.m

Hence by all these characteristics we can determine the lines are parallel, perpendicular or neither.

Note: By seeing the lines we can say which kind of line is it. Or we can prove that by following or by proving method the lines obey and then we can classify the lines. The parallel, perpendicular or some other lines have some specified properties, based on that we classify the lines.