Table of Contents
A one-dimensional body that connects two points is known as a straight line. As long as the two points fall someplace on the straight line, they can be stretched indefinitely. Parallel lines are two straight lines that run parallel to each other but never intersect or touch.
A Brief Outline
The straight lines run parallel to each other and have the same perpendicular distance between them at all points along each line. As a result, no matter how long two parallel lines extend, the space between them remains constant.
The shortest distance between two lines can be computed using the distance formula if the lines are parallel or not. The distance between them is determined by the length of a straight line made from one line to a point on the other line.
Important Concepts
Any parallel lines drawn on the Cartesian plane must always meet the plain’s x or y-axis, allowing us to determine the distance between the two parallel lines and the perpendicular line. The perpendicular line segment connects two parallel lines and creates the shortest distance between them. Furthermore, we know that if two straight lines in nature are parallel, their slopes will be equal.
To determine the distance between two parallel lines, skip the following steps: It’s crucial to check whether the parallel lines are written in slope-intercept form (y=mx+c). In the event that the equation is not given, it must be changed to this form by changing the variables. After that, you must determine the value of the points of intersection of two parallel lines. The slope value would be the same for both lines, as previously stated. Once you’ve computed all of these, you can plug them into the slope-intercept equation to get the value of y.
The distance between two lines can be estimated using the distance formula once the value of y has been determined. The equations of two parallel lines are in the slope-intercept form, as we know.
Y=mx+c1 …………… (1)
Y=mx+c2 …………… (2)
Significance of distance between 2 parallel lines in IIT JEE exam
The distance between two parallel lines is a less important topic that requires a solid understanding of equations. They will only respond to questions based on equations. Around 1 to 2 questions will be asked on the IIT JEE exam, which accounts for 3.3 percent of the total.
FAQs
First and foremost, they must both be straight lines that never cross. Second, there must always be the same distance between two parallel lines. Finally, the slopes of the two lines must be the same.
No, because parallel lines never cross, they don't have any solutions.
If the two lines never meet and are always equidistant from one another, they are said to be parallel to each other. What are the conditions that must be met for two lines to be deemed parallel to one another?
Will there be no solution for parallel lines?
What will the consequence be if two lines are parallel?
