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#### karush

##### Well-known member

- Jan 31, 2012

- 2,820

Show that the shortest distance from the point $\left(x_1,y_1\right)$ to a straight line

$$Ax_1+By_1+C=0$$ is

$$\frac{|Ax_1+By_1+C|}{\sqrt{A^2+B^2}}$$

ok, well a line from a point to a line is shortest if it is perpendicular to that line

obviously we are trying to find out a min value to this but taking a derivative of this without numbers is rather daunting and the question is asking for a proof

anyway not much of a start, but caught in the bushes already...

I did read the commentary on

"Finding the distance between a point and a line"

but this problem is under applications of differentiation which seem hard to set up

the book didn't give an answer to this...

$$Ax_1+By_1+C=0$$ is

$$\frac{|Ax_1+By_1+C|}{\sqrt{A^2+B^2}}$$

ok, well a line from a point to a line is shortest if it is perpendicular to that line

obviously we are trying to find out a min value to this but taking a derivative of this without numbers is rather daunting and the question is asking for a proof

anyway not much of a start, but caught in the bushes already...

I did read the commentary on

"Finding the distance between a point and a line"

but this problem is under applications of differentiation which seem hard to set up

the book didn't give an answer to this...

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