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Name: Ani
Status: student	
Age:  14
Location: N/A
Country: N/A
Date: N/A 


Question:
What is the formula for the distance between point A(x,y) and the line of equation y=mx+b.



Replies:
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.

Have fun!

Dr. Robinson


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.

AK

Dr. Ali Khounsary
Advanced Photon Source
Argonne National Laboratory
Argonne, IL 60439



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