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

1. ash2326 Group Title

@virtus Are you here?

2. virtus Group Title

yes!

3. ash2326 Group Title

@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 Group Title

sure, thanks ash2326

5. waterineyes Group Title

Can I give the formula??

6. ash2326 Group Title

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

7. waterineyes Group Title

8. ash2326 Group Title

|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 Group Title

yes

10. ash2326 Group Title

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 Group Title

POI

12. ash2326 Group Title

POI???

13. virtus Group Title

find the Point Of Intersection

14. waterineyes Group Title

Ha ha ha ha..

15. ash2326 Group Title

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 Group Title

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

17. virtus Group Title

oh wait do we know what C is ?

18. ash2326 Group Title

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

19. virtus Group Title

x+3y-15=0

20. ash2326 Group Title

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 Group Title

oh silly me

22. ash2326 Group Title

No problem, :D find it again?

23. virtus Group Title

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

24. ash2326 Group Title

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 Group Title

D (-1,2)

26. ash2326 Group Title

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

27. ash2326 Group Title

That will be the perpendicular distance:D

28. virtus Group Title

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

29. ash2326 Group Title

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

30. virtus Group Title

thanks so much for your invaluble help @ash2326 :D

31. ash2326 Group Title

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

32. dpaInc Group Title

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.