Point and Line Equation
What is the formula for the distance between point A(x,y)
and the line of equation y=mx+b.
1) A(x,y) lies on a line L perpendicular to y = mx + b.
2) L has slope - 1/m.
3) Use point-slope equation of straight line to obtain
equation for L.
4) Solve L and y = mx + b simultaneously to get point
B(x,y) on y = mx + b that is nearest A(x,y).
5) Now use distance formula on the points A and B.
The distance between a given point A(x0,y0) and a line ax+by+c=0 is
d = absolute value of [(ax0+by0+c)/sqrt(a^2+b^2)]
Just change the y=mx+b equation into the ax+by+c=0 form.
Dr. C. Murphy
This is a text-book problem. Since the new line is perpendicular to the
old line, its slope is -1/m. The new line, furthermore, passes through the
point A. With this information, you can find the constant C in the
equation of the line, y=(-1/m)x+C.
Dr. Ali Khounsary
Advanced Photon Source
Argonne National Laboratory
Argonne, IL 60439
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Update: June 2012