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Perpendicular Line Calculator
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Two lines are said to be perpendicular lines if they intersect to form a right angle. Perpendicular Line Calculator will help us to find to the perpendicular equation which passes through a particular point.
 

Steps for Perpendicular Line Calculator

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Step 1 :  

Find the slope of the given equation.


If the equation of the line $\Rightarrow$ ax + by + c = 0, the slope is given by $\frac{-a}{b}$ then the perpendicular slope is given by $\frac{-1}{\frac{-a}{b}}$ = $\frac{b}{a}$



Step 2 :  

Use point slope form to find the perpendicular equation of the line.



Problems on Perpendicular Line Calculator

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  1. Find the equation of the line that is perpendicular to the line x + y = 1 and passes through the point (2, 4)?


    Step 1 :  

    Given equation = x + y = 1


    Slope = $\frac{-a}{b}$$\frac{-1}{1}$ = -1


    Perpendicular slope = $\frac{-1}{-1}$ = 1 = m



    Step 2 :  

    Perpendicular equation of the line of slope(m) = 1 and passing through (2, 4)


    y - y1 = m(x - x1)


    y - 4 = 1(x - 2)


    y = x -2 + 4


    y = x + 2



    Answer  :  

    y = x + 2



  2. Find the equation of the line that is perpendicular to the line 4x + 8y = 1 and passes through the point (-1, 1)?


    Step 1 :  

    Given equation = 4x + 8y = 1


    Slope = $\frac{-a}{b}$$\frac{-4}{8}$ = $\frac{-1}{2}$


    Perpendicular slope = $\frac{-1}{\frac{-1}{2}}$ = 2 = m



    Step 2 :  

    Perpendicular equation of the line of slope(m) = 2 and passing through (-1, 1)


    y - y1 = m(x - x1)


    y - 1 = 2(x + 1)


    y = 2x + 2 + 1


    y = 2x + 3



    Answer  :  

    y = 2x + 3



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