find the distance from the line 4x+3y=5 to the point (6,9)

- anonymous

find the distance from the line 4x+3y=5 to the point (6,9)

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- anonymous

distance equation?

- 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

perhaps try this.

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## More answers

- 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

\[d=\frac{ \left| 4(6)+3(9)-5 \right| }{ \sqrt{4^2+3^2} }\]

- anonymous

been a while since I've done this so please correct me if i'm wrong

- 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

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

- oh the parallel line ! sorry

- anonymous

so was it right or wrong?

- welshfella

chrs00's method is correct and that comes to 9.2

- anonymous

yep

- welshfella

why did you use (0,5/3) on the original line?

- 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

distance=shortest distance

- 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

Chris00 formula gives you just that

- anonymous

you were given a point that did not lie on that line

- 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

ok

- anonymous

can u sketch it?

- welshfella

you can sketch it on the desmos web site

- anonymous

but i wouldnt get desmos to use in my test

- welshfella

the 2 parallel lines will look something like
|dw:1444387746919:dw|

- anonymous

ok

- 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

|dw:1444384572508:dw|

- welshfella

yea - did they give you that point (0. 5/3)?

- anonymous

no

- anonymous

i get that from the equation 4x+3y=5

- 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

ok

- anonymous

thank you both

- anonymous

: )

- 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

good luck in your studies

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