Properties of Parallel Lines
Some of the common properties of parallel lines are:
- Parallel lines have the same slope.
- The distance between parallel lines remains constant.
- Parallel Lines never intersect each other at a common point.
- Parallel Lines lie in the same plane.
- Parallel lines are often denoted by a symbol (∥) placed between the lines, indicating that they are parallel.
Equation of Parallel Lines
An equation such as y = mx + c, where c is the y-intercept and “m” is the slope of the line, is utilized to represent a straight line. Since two parallel lines are always have the same steepness i.e., their slopes are always equal. Thus, equation of two parallel lines can be written as
y = mx + c1 and y = mx + c2
Where c1 and c2 are the y-intercept of lines.
Example: Find the equation of parallel line to y = 4x – 3 which passes through (2, 12).
Solution:
Equation of line passing through (x1, y1) with slope m is y − y1 = m(x − x1).
Given: Equation of line y = 4x – 3
Slope of this line = 4
As we know, for parallel lines slope remains the same thus, m1 = m2 = 4.
Therefore, equation of required parallel line is y − 5 = 2(x − 4)
⇒ y − 5 = 2x − 8
⇒ 8 − 5 = 2x – y
⇒ 3 = 2x – y
Thus, the required equation is 2x – y = 3.
Parallel and Perpendicular Lines
Parallel and Perpendicular Lines are two sides of one coin. Perpendicular lines are intersecting lines, whereas parallel lines never intersect. Parallel lines in geometry are lines that never intersect and are always at the same distance from each other. On the other hand, perpendicular lines are lines that intersect each other at a right angle, forming a 90° angle. In this article, we will discuss these in detail, including examples and differences.
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