How do I find a standard equation of a perpendicular line with just the points (5,1)?

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

It is not possible to find the equation of a perpendicular line given just one point. There are an infinite number of lines that pass through any given point. To uniquely define a line it is essential to have two points that lie on the line. And unless a unique line and a unique point on the line are known it is not possible to determine the equation of a perpendicular line.

Given just a point (5, 1) it is not possible to determine the equation of a perpendicular line.

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anya4one | Student, Undergraduate | (Level 2) Honors

Posted on

Thank you.  I thought so too, just wanted to confirm.

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aruv | High School Teacher | (Level 2) Valedictorian

Posted on

Through given point (5,1) ,an infinite number of lines can be drawn so consequently an infinite number of perpendicular lines too can be found.

If we assume a general equation

y=mx+c  ,which posses through (5,1)

then a perpendicular line ,perpendicular to it will be

y-1=(-1/m)(x-5)       .

so find unique line  we  two given conditions.

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