## anonymous 4 years ago Find the distance from (2,-1) to the line y=2x+3. The answer is 8/5*root5 by the way, but I want to know how to solve. I used distance formula. sqrt ( (x-2)^2 + (y+1)^2) sqrt ( (x-2)^2 + (2x+3+1)^2) sqrt ( (x-2)^2 + (2x+4)^2) sqrt (5x^2 + 12x + 20) When I enter this on my calculator to solve for x, it cannot do it. What should I do next?

1. anonymous

you don't use X

2. precal

What kind of calculator are you using? Are you using the solve feature?

3. anonymous

Yes I am usin the solve feature.

4. precal

Why don't you use graph paper instead?

5. anonymous

I have to use algebraic methods and show my work.

6. precal

graphing on graph paper is a way to show your work

7. anonymous

Is there a way to answer the problem algebraically?

8. anonymous

Well, the line to the other linen willl be perpendicular to it

9. anonymous

Assuming you want the shortest distance

10. precal

using graph paper is a valid method, then you can count the number of units

11. anonymous

Find the equation of a line perpendicular to y=2x+3 and use the distance formula on the intersection

12. precal

You could use a point from the equation. I would graph it to decide what point to use. You need two ponts for the distance formula

13. Mertsj

Have you studied the formula for finding the perpendicular to a line through a point?

14. anonymous

Well, I'm in Calculus right now, but I don't know how to continue this problem.

15. precal

Yep calculus would study that Do the normal line

16. anonymous

Wouldn't the normal slope be -1/2 ?

17. anonymous

-1/2*

18. anonymous

$y+1=\frac{-1}{2}(x-2)$

19. anonymous

$y=-\frac{1}{2}x$

20. Mertsj

You could put the equation in the form Ax+By=C=0 and use this formula: $d=\frac{|Am+Bn+C|}{\sqrt{A ^{2}+B ^{2}}}$ The point is (m,n)

21. anonymous

Now set 2x+3=-(1/2)x to find the intersection, then use the distance formula

22. anonymous

x = -6/5

23. anonymous

Get y now, and use this point in your distance formula

24. precal

Mertsj what formula did you post? Do you know the name of it? Just curious

25. Mertsj

Perpendicular distance from a Point to a Line

26. precal

ok I have not seen that one before. Good to know

27. anonymous

Okay I now have two methods of approaching this problem. Thank you all for helping me. :)