SOLUTION: AB is perpendicular to BN. B=(3,4), A=(0,0). What are the coordinates of N if N is on the x axis? thank you so much for your time!

Question 245499: AB is perpendicular to BN. B=(3,4), A=(0,0). What are the coordinates of N if N is on the x axis?
thank you so much for your time!
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

The first thing you need is the slope of the line containing the segment AB.

Use the slope formula:

where

and

are the coordinates of A and B.

Then you need an equation of the line that contains the segment BN. Since you know that BN is perpendicular to AB, use the slope you calculated above and the fact that perpendicular lines have slopes that are negative reciprocals of each other, in other words:

Plus the fact that such a line must pass through point B along with the point slope form of the equation of a line to derive the desired equation:

Where

is the negative reciprocal of the slope you calculated in the first step of this procedure and

are the coordinates of point B.

Now all you need is the intersection of the line represented by the equation you just derived and the

-axis. Substitute 0 for y and solve the resulting single variable equation for x. Point N will be the ordered pair

where

is equal to the value of

in the equation when

John

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