## anonymous one year ago find the distance from the line 4x+3y=5 to the point (6,9)

1. anonymous

distance equation?

2. anonymous

m=-4/3 y-9=-4/3(x-6) y-9=-4/3x+8 y=-4/3x +17 (0, 5/3) and (6,9) d=s.rt (6-0)^2+(9-5/3)^2 =9.47511

3. anonymous

perhaps try this.

4. anonymous

The distance from a point P(x,o,yo) to a line ax+by+c = 0 is $d=\frac{ \left| ax _{o}+by _{o}+c \right| }{ \sqrt{a^2+b^2} }$

5. anonymous

$d=\frac{ \left| 4(6)+3(9)-5 \right| }{ \sqrt{4^2+3^2} }$

6. anonymous

been a while since I've done this so please correct me if i'm wrong

7. anonymous

i got 9.2... but the hint say first find the line through the point (6,9) parallel to the given line, and then find the distance between these lines

8. welshfella

you made a slight error on the slope of the line perpendicular to the given line its slope is - 1 / (-4/3) = 3/4

9. welshfella

- oh the parallel line ! sorry

10. anonymous

so was it right or wrong?

11. welshfella

chrs00's method is correct and that comes to 9.2

12. anonymous

yep

13. welshfella

why did you use (0,5/3) on the original line?

14. anonymous

i think he just used any point on that line. i think you need to use a point that is perpendicular to that line

15. anonymous

distance=shortest distance

16. anonymous

are u sure ..this question is structure different frm the previous set of questions that i did..they want .. to find distance frm the point (a,b) eg.(4,8) to the line y=sumthing eg 6x+8y=9 ... inwhich i used that formula provide by chrs00 but the question ask to find the distance frm the line given to the point given...

17. welshfella

Chris00 formula gives you just that

18. anonymous

you were given a point that did not lie on that line

19. welshfella

another way to do it is to find the equation of the line perpendicular to the original line and passing through the point (6,9) then solving the 2 equations simultaneously to find the point of intersection. Then use the distance formula with this point and (6,9) But that's a bit long-winded.

20. anonymous

ok

21. anonymous

can u sketch it?

22. welshfella

you can sketch it on the desmos web site

23. anonymous

but i wouldnt get desmos to use in my test

24. welshfella

the 2 parallel lines will look something like |dw:1444387746919:dw|

25. anonymous

ok

26. welshfella

the line joining the point (0, 5/3) and (6,9) is not perpendicular to the 2 parallel lines. That is why you didn't get the right answer

27. anonymous

|dw:1444384572508:dw|

28. welshfella

yea - did they give you that point (0. 5/3)?

29. anonymous

no

30. anonymous

i get that from the equation 4x+3y=5

31. welshfella

yes i see Well you cant take any old point . The line joining the point to (6,9) must be perpendicular ( shortest distance)

32. anonymous

ok

33. anonymous

thank you both

34. anonymous

: )

35. welshfella

the formula that chris00 used is the easiest way to do it. Finding the line perpendicular etc ( the way i mentined) is long and messy yw

36. anonymous