Question:
The distance between the parallel lines $ y=x+a,\,\,y=x+b $ is
The distance between the parallel lines $ y=x+a,\,\,y=x+b $ is
Updated On: Jun 23, 2024
- $ \frac{|b-a|}{\sqrt{2}} $
- $ |a-b| $
- $ |a+b| $
- $ \frac{|a+b|}{\sqrt{2}} $
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The Correct Option is A
Solution and Explanation
The distance between two parallel lines
$ =\frac{|{{c}_{1}}-{{c}_{2}}|}{\sqrt{{{a}^{2}}+{{b}^{2}}}} $
$ \therefore $ Distance $ =\frac{|b-a|}{\sqrt{{{1}^{2}}+{{1}^{2}}}} $ $ =\frac{|b-a|}{\sqrt{2}} $
$ =\frac{|{{c}_{1}}-{{c}_{2}}|}{\sqrt{{{a}^{2}}+{{b}^{2}}}} $
$ \therefore $ Distance $ =\frac{|b-a|}{\sqrt{{{1}^{2}}+{{1}^{2}}}} $ $ =\frac{|b-a|}{\sqrt{2}} $
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Concepts Used:
Horizontal and vertical lines
Horizontal Lines:
- A horizontal line is a sleeping line that means "side-to-side".
- These are the lines drawn from left to right or right to left and are parallel to the x-axis.
Equation of the horizontal line:
In all cases, horizontal lines remain parallel to the x-axis. It never intersects the x-axis but only intersects the y-axis. The value of x can change, but y always tends to be constant for horizontal lines.
Vertical Lines:
- A vertical line is a standing line that means "up-to-down".
- These are the lines drawn up and down and are parallel to the y-axis.
Equation of vertical Lines:
The equation for the vertical line is represented as x=a,
Here, ‘a’ is the point where this line intersects the x-axis.
x is the respective coordinates of any point lying on the line, this represents that the equation is not dependent on y.
⇒ Horizontal lines and vertical lines are perpendicular to each other.