## karatechopper 3 years ago How to find distance between two lines... y=3x y=3x+10

1. zonazoo

the vertical distance, or horizontal distance or what?

2. karatechopper

|dw:1350957364620:dw|

3. zonazoo

that perpendicular line between the two is the distance you want?

4. asnaseer

Work out the equation of the perpendicular line. To make t easy, work out the equation of the line that is perpendicular to y=3x and passes through (0,0). Then find the intersection point of this perpendicular line and the other line (y=3x + 10). Then use distance formula.

5. asnaseer

Hope that makes sense?

6. zonazoo

yeah, thats what i would do

7. karatechopper

I am very confused papa. Things are not going well in my house. So can you restart from baby steps? And walk me through the perpendicular lines?

8. asnaseer

ok, step 1 - do you know the relationship of the slopes of two lines that are perpendicular to one another?

9. karatechopper

I know that the perpendicular slope is the opposite reciprocal of the slope.

10. asnaseer

almost - the product of the slopes of two perpendicular lines is always -1.

11. asnaseer

so - what would be the slope of the line that is perpendicular to y=3x?

12. karatechopper

-1/3x

13. asnaseer

perfect - slope would be -1/3, and its equation would be of the form: y = -(1/3)x + c where c is the y-intercept

14. asnaseer

agreed?

15. karatechopper

Correct. I got that part.

16. asnaseer

good, now if we take this perpendicular line such that it passes through the origin, then what would be the value for c?

17. asnaseer

remember we have: y = -(1/3)x + c and we know y=0 when x=0, therefore c=?

18. asnaseer

are you stuck?

19. karatechopper

yes..

20. karatechopper

C=0

21. asnaseer

yes - correct

22. karatechopper

Yay!

23. asnaseer

so now we know that the line perpendicular to y=3x and that passes through the origin has the equation: y = -(1/3)x

24. karatechopper

Ok, so i drew that line in on my graph..

25. karatechopper

|dw:1350958743362:dw|

26. asnaseer

|dw:1350951532761:dw|

27. karatechopper

Yea! That!

28. asnaseer

so next you want to find the point of intersection of: y = -(1/3)x and: y = 3x + 10

29. karatechopper

Oh ok !

30. karatechopper

How do i do that...

31. asnaseer

can you find the point of intersection of these two lines?

32. asnaseer

just substitue y=-(1/3)x from 1st equation into 2nd equation and solve for x.

33. asnaseer

then use 1st equation to find the y value once you have the x value

34. karatechopper

Ah ok!

35. karatechopper

So like....the answer would be for x=3?

36. asnaseer

make sure you have the correct sign - does it look like x would be positive here?

37. karatechopper

aahhhh!!! negative negative!!

38. asnaseer

:)

39. asnaseer

now find y value

40. asnaseer

use the first equation for that, i.e. y = -(1/3)x to find y. remember you just found x=-3

41. karatechopper

Oh i know i am working it out!!!

42. karatechopper

y=19

43. asnaseer

how???

44. asnaseer

x=-3, therefore:$y=-\frac{1}{3}\times x=-\frac{1}{3}\times (-3) = ?$

45. karatechopper

Oh ok i was using a dif equation.

46. karatechopper

y=-1

47. asnaseer

48. karatechopper

gAAAA

49. karatechopper

Ohhhhhhhh y=1

50. asnaseer

good. so now you know the point of intersection is (-3, 1): |dw:1350952783534:dw|

51. asnaseer

so just use the distance formula to find the distance between (-3,1) and (0,0). That will be the distance between these two lines.

52. karatechopper

Alright thanks!

53. asnaseer

yw :)

54. karatechopper

Now SLEEP! I am ordering my papa to sleep:)