anonymous
  • anonymous
Find the distance from the point of intersection of the lines 2x+3y=10 and 3x-y=4 to the line 5x-6y=1
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • 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
anonymous
  • 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?
anonymous
  • 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

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anonymous
  • anonymous
oops.. the ax by and c terms chould all be squared under the root
anonymous
  • anonymous
actually looking again.. they aren't squared. the first formula is right
anonymous
  • anonymous
(without the square root)
anonymous
  • anonymous
yeah That's the formula I have
anonymous
  • anonymous
so the equation is actually just |ax +by+c| / sqrt(a^2 + b^2 )
anonymous
  • anonymous
But I'm supposed to use the absolute value, right?
anonymous
  • anonymous
yeah
anonymous
  • anonymous
and that's what I think was making me do the question wrong
anonymous
  • anonymous
so it should be 3 right?
anonymous
  • anonymous
not -3
anonymous
  • anonymous
Yeah, but the answer is 0.38
anonymous
  • anonymous
So does the absolute value apply to the denominator too?
anonymous
  • anonymous
Well both terms are squared so it won't matter for the bottom
anonymous
  • anonymous
So... The bottom should be ... \[\sqrt{61}\] right?
anonymous
  • anonymous
yeah
anonymous
  • anonymous
Hallelujah the right answer! Finally :) Thanks for your help :)
anonymous
  • anonymous
awwyeah :)

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