## anonymous 5 years ago Find the distance from the point of intersection of the lines 2x+3y=10 and 3x-y=4 to the line 5x-6y=1

1. anonymous

First find the point set both your equations equal and solve for (x,y) (you could probably even get it by guessing) Then use the distance formula from a point to a line

2. anonymous

The point is 2,2 but I think I'm using the formula for the distance from a point to a line incorrectly... Could you show me how you'd do it?

3. anonymous

Okay, the point is (2,2) and the line is 5x-6y=1 So the formula you can use is just $\sqrt{ax+by+c} \div \sqrt{a ^{2}}+b ^{2}$ Where the point is (x,y) and the line is ax+by+c=0

4. anonymous

oops.. the ax by and c terms chould all be squared under the root

5. anonymous

actually looking again.. they aren't squared. the first formula is right

6. anonymous

(without the square root)

7. anonymous

yeah That's the formula I have

8. anonymous

so the equation is actually just |ax +by+c| / sqrt(a^2 + b^2 )

9. anonymous

But I'm supposed to use the absolute value, right?

10. anonymous

yeah

11. anonymous

and that's what I think was making me do the question wrong

12. anonymous

so it should be 3 right?

13. anonymous

not -3

14. anonymous

Yeah, but the answer is 0.38

15. anonymous

So does the absolute value apply to the denominator too?

16. anonymous

Well both terms are squared so it won't matter for the bottom

17. anonymous

So... The bottom should be ... $\sqrt{61}$ right?

18. anonymous

yeah

19. anonymous