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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

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

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