## karatechopper Group Title How to find distance between two lines... y=3x y=3x+10 one year ago one year ago

1. zonazoo Group Title

the vertical distance, or horizontal distance or what?

2. karatechopper Group Title

|dw:1350957364620:dw|

3. zonazoo Group Title

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

4. asnaseer Group Title

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 Group Title

Hope that makes sense?

6. zonazoo Group Title

yeah, thats what i would do

7. karatechopper Group Title

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 Group Title

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

9. karatechopper Group Title

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

10. asnaseer Group Title

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

11. asnaseer Group Title

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

12. karatechopper Group Title

-1/3x

13. asnaseer Group Title

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 Group Title

agreed?

15. karatechopper Group Title

Correct. I got that part.

16. asnaseer Group Title

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 Group Title

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

18. asnaseer Group Title

are you stuck?

19. karatechopper Group Title

yes..

20. karatechopper Group Title

C=0

21. asnaseer Group Title

yes - correct

22. karatechopper Group Title

Yay!

23. asnaseer Group Title

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 Group Title

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

25. karatechopper Group Title

|dw:1350958743362:dw|

26. asnaseer Group Title

|dw:1350951532761:dw|

27. karatechopper Group Title

Yea! That!

28. asnaseer Group Title

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

29. karatechopper Group Title

Oh ok !

30. karatechopper Group Title

How do i do that...

31. asnaseer Group Title

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

32. asnaseer Group Title

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

33. asnaseer Group Title

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

34. karatechopper Group Title

Ah ok!

35. karatechopper Group Title

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

36. asnaseer Group Title

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

37. karatechopper Group Title

aahhhh!!! negative negative!!

38. asnaseer Group Title

:)

39. asnaseer Group Title

now find y value

40. asnaseer Group Title

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

41. karatechopper Group Title

Oh i know i am working it out!!!

42. karatechopper Group Title

y=19

43. asnaseer Group Title

how???

44. asnaseer Group Title

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

45. karatechopper Group Title

Oh ok i was using a dif equation.

46. karatechopper Group Title

y=-1

47. asnaseer Group Title

48. karatechopper Group Title

gAAAA

49. karatechopper Group Title

Ohhhhhhhh y=1

50. asnaseer Group Title

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

51. asnaseer Group Title

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 Group Title

Alright thanks!

53. asnaseer Group Title

yw :)

54. karatechopper Group Title

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