## anonymous 4 years ago Find the shortest distance from the line 2x+6y=3 and passing through the point (9,-7)

1. Mertsj

That would be the perpendicular distance so you must first find the equation of the perpendicular through( 9,-7) that has slope 3.

2. Mertsj

Do that and we'll go from there.

3. anonymous

can yu show me how to do it?

4. anonymous

If memory serves, $$\huge \frac{ 2(9)+6(-7)-3 } { \pm \sqrt{2^2+6^2 } }$$

5. Mertsj

Can you find the equation of a line whose slope is 3 and contains the point (9,-7)?

6. Mertsj

Oh. I see that Fool wants to help you now so I'll turn you over to him.

7. anonymous

lol yu can still help me

8. anonymous

im not sure if yur suppose to use the quadratic formula for this

9. Mimi_x3

THe formula for this, i think: $\large \frac{ax_{1}+by_{1}+c}{\sqrt{a^{2}+b^{2}}}$

10. anonymous

there is a formula for it

11. anonymous

The proof requires representing the lines in normal form and then finding the perpendicular distances.

12. anonymous

Mimi, your formula is close but not apt, it should be Either, $\large \pm\frac{ax_{1}+by_{1}+c}{\sqrt{a^{2}+b^{2}}}$ or $\large \frac{|ax_{1}+by_{1}+c|}{\sqrt{a^{2}+b^{2}}}$ Recall, Euclidean distance cannot be negative :)

13. Mimi_x3

lol, yeah i forgot my bad.

14. anonymous

no worries, as long as you give me medal :P

15. Mimi_x3

obssessed of medals huh :P

16. anonymous

whats the point of medals? do yu get nythin

17. anonymous

hehe, not really it's fun though.

18. Mimi_x3

You get nothing, just a level, it just a waste of time anyway :P

19. anonymous

Why should I answer you? Will I get anything? What is the purpose of anything in life? Life is as meaningless itself as this discussion :P

20. anonymous

LMAO ^

21. Mimi_x3

Lol, life is cruel.

22. anonymous

;)