## anonymous 5 years ago What is the distance from the point (6,0) to the line y=3x+2?

1. amistre64

which distance you want? shortest most likly

2. amistre64

the shortest distance is a perpendicular line....

3. amistre64

so to find it, we need the line that is perp to this and the point they intersect

4. anonymous

Possible answers are 4, $2\sqrt{10} , \sqrt{26} , and\ 3\sqrt{6}$ so I guess which ever equals one of those

5. amistre64

the perp has a product of slopes that equals -1 3x = -1 x = -1/3 0 = -1/3(6) +b b = 2 y = (-1/3)x +2

6. amistre64

these lines meet at: 3x+2 = (-1/3)x +2 3x + 1/3x = 0 10/3x = 0 x = 0

7. amistre64

they appear to meet at the origin...

8. amistre64

they meet at (0,2) if anything lol

9. amistre64

id go with 4

10. anonymous

Per distance formula is $d= \frac{ \left| ax +by +c \right| }{ \sqrt{a^2 +b^2}}$

11. amistre64

im prolly wrong since i guessed that lol

12. amistre64

y = 3x+2 ..... 0 = -6/3 +b 0 = -2 +b b = 2 y = (-1/3)x +2.... that seems to work out

13. anonymous

y= 3x+2 get into general form 3x - y + 2 =0 so this means that a=3 , b=-1 and c=2 in our formulas above, and (x,y) are the coordinates of the point ( 6,0) so x=6 , y=0

14. anonymous

d= (9 +2 ) / 2 = 4.5 units

15. anonymous

wait thats wrong

16. amistre64

3x+2 = (-1/3)x +2 3x = -1/3x when x=0 right?

17. amistre64

(0,2) (6,0) 36 + 4 = 40 = sqrt(40)

18. amistre64

2sqrt(10)

19. amistre64

got it ;)

20. anonymous

d = $\frac { \left| 3(6) + 0 + 2 \right|}{\sqrt{10} }$

21. amistre64

22. anonymous

20/ sqrt (10)

23. anonymous

wtf

24. amistre64

20sqrt(10) --------- 10

25. anonymous

yes I know

26. amistre64

2 sqrt(10)

27. amistre64

need a calculator? :)

28. anonymous

Very puzzling question lol

29. amistre64

just had to get the sleep of my ears to see what i was doin

30. anonymous

Well thank you