## virtus 2 years ago perpendicular distance from point B(0,5) to the line x+3y-5=0

1. ash2326

@virtus Are you here?

2. virtus

yes!

3. ash2326

@virtus There maybe a direct formula for this, but I don't remember that. I'll start from the basics. Do you have time for this?

4. virtus

sure, thanks ash2326

5. waterineyes

Can I give the formula??

6. ash2326

Thanks virtus, let's begin. I recommend that you understand the problem, you'll remember it always. What do you want?

7. waterineyes

Go ahead @ash2326 ..

8. ash2326

|dw:1341645333105:dw| Let AB be our line and C is the point for which we need to find the perpendicular distance. Do you understand the diagram?

9. virtus

yes

10. ash2326

You can see that the perpendicular line from the point C is intersecting the line AB at a point. Let it be D If we could find the coordinates of D, then we can easily find the distance. do you have any ideas what should we do?

11. virtus

POI

12. ash2326

POI???

13. virtus

find the Point Of Intersection

14. waterineyes

Ha ha ha ha..

15. ash2326

Yeah:) @virtus For that we need to find the equation of the line CD, do you have any idea how to do that?

16. virtus

well you know what point C is and the gradient of line CD would be -1/ gradient of line AB

17. virtus

oh wait do we know what C is ?

18. ash2326

Awesome:D Could you do that? We have AB as $$x+3y-5=0$$ Yeah we know C as (0, 5)

19. virtus

x+3y-15=0

20. ash2326

Oops, You made a mistake I can see that perpendicular line's slope is same as AB, it's to be -1/ slope AB Check again :)

21. virtus

oh silly me

22. ash2326

No problem, :D find it again?

23. virtus

y-5 =3(x-0) y=3x +5 3x-y+5=0

24. ash2326

Correct:D Now find the intersection of the line (3x-y+5=0) and (x+3y-5=0) this will give us D

25. virtus

D (-1,2)

26. ash2326

Great work:D now find the distance between (0, 5) and (-1, 2) using distance formula.

27. ash2326

That will be the perpendicular distance:D

28. virtus

ngawwwwwww! I SEE!!!! so that's how you do it ;) oh btw i got square root 10

29. ash2326

Yeah, that's correct:D Great work btw:D

30. virtus

thanks so much for your invaluble help @ash2326 :D

31. ash2326

@virtus you did all the work. I just guided you:D You are a good student:D

32. dpaInc

you can also use the formula from analytic geometry that the distance from a given point to a given line in general form $$\large Ax+By+C=0$$ is given by Distance = $$\large \frac{Ax_0+By_0+C}{\pm \sqrt{A^2+B^2}}$$ where $$\ (x_0, y_0)$$ are the coordinates of the given point.