Perpendicular lines definition | Perpendicular lines examples
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The Perpendicular Line an online tool which shows Perpendicular Line for the given input. Byju's Perpendicular Line is a tool which makes calculations very simple and interesting. If an input is given then it can easily show the result for the given number.

Byju’s perpendicular line calculator is an online tool which makes the calculation easy and brisk thereby saving time for tedious calculations. All you have to do is enter the equation of line and the coordinates through which the perpendicular line will pass. You will get the equation of the perpendicular line in seconds. The working of this calculator is explained as follows:In the figure , we have two lines l1 and l2 with inclinations α , β. If they are perpendicular , we can say that β=α+90°. (Using properties of angles)

Their slopes can be given as m1=tan(α+90°) andm2=tan⁡α.

⇒m_1=-cot⁡α=-1/tan⁡α = -1/m_2

⇒m_1=-1/m_2

⇒m_1×〖 m〗_2=-1

Thus , for two lines to be perpendicular the product of their slope must be equal to -1.

If the equation of the two lines is given by ax+by+c=0 and a’ x+b' y+c'=0 , these lines are perpendicular to each other if and only if , aa'+bb'=0. (Again , we can arrive at this result if you find the slopes of each line and equate their product to -1.)

Thus Byju’s calculator determines the slope of the perpendicular line using m1m2 = -1 and then equation of the perpendicular line passing through the given point and given line can be determined using the point slope form of line y – y1 = m(x – x1).

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