Math Is Fun Forum

Hannibal lecter

Member

Registered: 2016-02-11

Posts: 392

perpendicular lines

equation for the line through the point (2,1) which is perpendicular to the line y =5x−3.
the slope for this line is 5
that's mean the slope of the equation will be : - 1/5
because it's perpendicular  on the other

what is the proof for that? why -1/5?
and why ( mines - )?

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Wisdom is a tree which grows in the heart and fruits on the tongue

Bob

Administrator

Registered: 2010-06-20

Posts: 10,143

Re: perpendicular lines

Try this:

Sketch a set of coordinate axes and mark the general point (x,y) in the first quadrant. Make a rectangle by joining the points (0,0), (x,0), (x,y) and (0,y).

Now rotate the rectangle 90 anticlockwise so that the new rectangle is in the second quadrant.  You'll see that the coordinates of the new shape are (0,0), (0,x), (-y,x) and (-y,0).

The gradient of the line joining (0,0) to (x,y) is y/x.  The gradient joining (0,0) to (-y,x) is x/-y

So the product of the gradients is y/x times x/-y =-1

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
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George,Y

Member

Registered: 2006-03-12

Posts: 1,379

Re: perpendicular lines

tan(a+pi/2) = sin(a + pi/2) / cos(a+pi/2) = cos(a) / -sin(a) = -1/tan(a)

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X'(y-Xβ)=0