anonymous
  • anonymous
find the distance from the line 4x+3y=5 to the point (6,9)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
distance equation?
anonymous
  • anonymous
m=-4/3 y-9=-4/3(x-6) y-9=-4/3x+8 y=-4/3x +17 (0, 5/3) and (6,9) d=s.rt (6-0)^2+(9-5/3)^2 =9.47511
anonymous
  • anonymous
perhaps try this.

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anonymous
  • anonymous
The distance from a point P(x,o,yo) to a line ax+by+c = 0 is \[d=\frac{ \left| ax _{o}+by _{o}+c \right| }{ \sqrt{a^2+b^2} }\]
anonymous
  • anonymous
\[d=\frac{ \left| 4(6)+3(9)-5 \right| }{ \sqrt{4^2+3^2} }\]
anonymous
  • anonymous
been a while since I've done this so please correct me if i'm wrong
anonymous
  • anonymous
i got 9.2... but the hint say first find the line through the point (6,9) parallel to the given line, and then find the distance between these lines
welshfella
  • welshfella
you made a slight error on the slope of the line perpendicular to the given line its slope is - 1 / (-4/3) = 3/4
welshfella
  • welshfella
- oh the parallel line ! sorry
anonymous
  • anonymous
so was it right or wrong?
welshfella
  • welshfella
chrs00's method is correct and that comes to 9.2
anonymous
  • anonymous
yep
welshfella
  • welshfella
why did you use (0,5/3) on the original line?
anonymous
  • anonymous
i think he just used any point on that line. i think you need to use a point that is perpendicular to that line
anonymous
  • anonymous
distance=shortest distance
anonymous
  • anonymous
are u sure ..this question is structure different frm the previous set of questions that i did..they want .. to find distance frm the point (a,b) eg.(4,8) to the line y=sumthing eg 6x+8y=9 ... inwhich i used that formula provide by chrs00 but the question ask to find the distance frm the line given to the point given...
welshfella
  • welshfella
Chris00 formula gives you just that
anonymous
  • anonymous
you were given a point that did not lie on that line
welshfella
  • welshfella
another way to do it is to find the equation of the line perpendicular to the original line and passing through the point (6,9) then solving the 2 equations simultaneously to find the point of intersection. Then use the distance formula with this point and (6,9) But that's a bit long-winded.
anonymous
  • anonymous
ok
anonymous
  • anonymous
can u sketch it?
welshfella
  • welshfella
you can sketch it on the desmos web site
anonymous
  • anonymous
but i wouldnt get desmos to use in my test
welshfella
  • welshfella
the 2 parallel lines will look something like |dw:1444387746919:dw|
anonymous
  • anonymous
ok
welshfella
  • welshfella
the line joining the point (0, 5/3) and (6,9) is not perpendicular to the 2 parallel lines. That is why you didn't get the right answer
anonymous
  • anonymous
|dw:1444384572508:dw|
welshfella
  • welshfella
yea - did they give you that point (0. 5/3)?
anonymous
  • anonymous
no
anonymous
  • anonymous
i get that from the equation 4x+3y=5
welshfella
  • welshfella
yes i see Well you cant take any old point . The line joining the point to (6,9) must be perpendicular ( shortest distance)
anonymous
  • anonymous
ok
anonymous
  • anonymous
thank you both
anonymous
  • anonymous
: )
welshfella
  • welshfella
the formula that chris00 used is the easiest way to do it. Finding the line perpendicular etc ( the way i mentined) is long and messy yw
anonymous
  • anonymous
good luck in your studies

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