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anonymous
 one year ago
find the distance from the line y6=m(x+1) to the point given below
anonymous
 one year ago
find the distance from the line y6=m(x+1) to the point given below

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[(\sqrt{(1+m^2)},6+\sqrt{(1+m^2)} )\]\[(1,4)\]and \[(2,1)\]these are the three given points

amistre64
 one year ago
Best ResponseYou've already chosen the best response.3what methods do you have available at your disposal?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I seeing this formula but not sure what to do..\[d=\frac{ Ax+By+C }{ \pm \sqrt{A^2+B^2} }\]

amistre64
 one year ago
Best ResponseYou've already chosen the best response.3i cant say i know what that refers to either ... but i have an idea on how to find a solution. we need to know the distance formula, how to determine a perpendicular slope, formulate a line equation from a point and a slope, and determine where 2 lines cross at.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok how do we do that

amistre64
 one year ago
Best ResponseYou've already chosen the best response.3another idea involves making a circle at a point, seeing where the line crosses it, and taking the midpoint, then distancing the results

amistre64
 one year ago
Best ResponseYou've already chosen the best response.3well, given a slope of a line: m 1/m creates a perpendicular slope ... for a given point (a,b), the form of the perp line is: 1/m(xa) +b finding where the two lines meet ... is equating them 1/m (xa) + b = m(x+1)+6 x/m +a/m + b = mx +m +6 a/m + b (m +6) = mx+x/m a/m + b (m +6) = x(m+1/m) (a/m + b (m +6))/(m+1/m) = x knowing x, we find y by substitution etc ...

amistre64
 one year ago
Best ResponseYou've already chosen the best response.3but if you can figure out that formula, and it is one for your course ... go for it :)

amistre64
 one year ago
Best ResponseYou've already chosen the best response.3dw:1443919404316:dw i think that formula of yours is from the distance between 2 planes tho

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0we don't know whats m

amistre64
 one year ago
Best ResponseYou've already chosen the best response.3m is just a general value ... the solution will be general as well

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so y=(a/m + b (m +6))/(m+1/m) ??

amistre64
 one year ago
Best ResponseYou've already chosen the best response.3given y = m(x+1)+6 and x = (a/m + b (m +6))/(m+1/m) , i hope i did that right :) y = mx + m + 6 mx = (a + bm m^2 +6m)/(m+1/m) = m(m^2 (6+b)m a)/(m^2+1) y = m(m^2 (6+b)m a)/(m^2+1) + m + 6 might be prudent to find the values for x and y before trying to process a general formula, it is starting to look messy

amistre64
 one year ago
Best ResponseYou've already chosen the best response.3lets use the (1,4) for (a,b)

amistre64
 one year ago
Best ResponseYou've already chosen the best response.3and for simplicity, assume a slope of 1 for brevity

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok so we can use any poits for (a,b)?

amistre64
 one year ago
Best ResponseYou've already chosen the best response.3x = (a/m + b (m +6))/(m+1/m) x = (1/1 + 4 (1 +6))/(1+1/1) x = (2)/(2) = 1 y = m(1+1)+6 = 6 well, (a,b) should be a stated point, since that is the one we are trying to define a line with and cross it

amistre64
 one year ago
Best ResponseYou've already chosen the best response.3http://www.wolframalpha.com/input/?i=y%3D1%28x%2B1%29%2B6%2C+y%3D1%28x1%29%2B4 the good news maybe that our formulas for finding the crossing point are good

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I think ill understand this ...if I wasn't this sleepy

amistre64
 one year ago
Best ResponseYou've already chosen the best response.3what is the distance from (1,4) to (1,6) ?

amistre64
 one year ago
Best ResponseYou've already chosen the best response.3but this assumes a slope; m=1

amistre64
 one year ago
Best ResponseYou've already chosen the best response.3trying to think of a vector way to approach it, or translation of the line so that we are finding the distance from the origin

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok if it work....but this is geometry though

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0we can use anything ..I guess

amistre64
 one year ago
Best ResponseYou've already chosen the best response.3well, y6 = m(x+1) can be dropped 6 units to pass thru the origin as y = m(x+1), since we drop the line, we drop the point by 6 as well (1,46) = (1,2) dw:1443922039651:dw

amistre64
 one year ago
Best ResponseYou've already chosen the best response.3\[\vec n=(a,b6)\] \[\vec \mu=(1,m )\] \[cos(\alpha)=\frac{a+m(b6)}{\sqrt{a^2+(b6)^2}~\sqrt{1+m^2} }\] \[\alpha=cos^{1}\left(\frac{a+m(b6)}{\sqrt{a^2+(b6)^2}~\sqrt{1+m^2} }\right) \] \[d=nsin(\alpha)\] \[d=\sqrt{a^2+(b6)^2}~sin(\alpha)\]

amistre64
 one year ago
Best ResponseYou've already chosen the best response.3lets test this thought out ... m=1, a=1,b=4 sqrt(1+4)sin(cos^(1)((1+1(2))/(sqrt(5)sqrt(2)))) well something went aloof, we didnt get 2 sqrt2 inthe simplification

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok I'm lost... I'm sleepy ...but I think m shd be 1

amistre64
 one year ago
Best ResponseYou've already chosen the best response.3m is the slope of the stated line ... we can simplify the process if we make it a concrete value like 1 or 1 but overall the distance solution required has to keep m general

amistre64
 one year ago
Best ResponseYou've already chosen the best response.3http://www.mathwords.com/d/distance_point_to_line.htm or this defines the parts of your formula for us

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yea that same formula I have here ...but idk

amistre64
 one year ago
Best ResponseYou've already chosen the best response.3y  6 = mx +m (m)x + (1)y = (m+6) A = m, B=1, C=m+6

amistre64
 one year ago
Best ResponseYou've already chosen the best response.3so we know ABandC, and stated point values ...

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0wait 1 sec ..let me comprehend this

amistre64
 one year ago
Best ResponseYou've already chosen the best response.3my C is off, foiled by a negative

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0y6=mx+m 6m=mxy (6+m)=mxy

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok so mxy+(6+m)=0 a=m b=1 c=(6+m) ok I see

amistre64
 one year ago
Best ResponseYou've already chosen the best response.3ugh, im tired too, im used to C being on the other side of =

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0no c=6+m remember we bring it back over the equal sign so it become positive

amistre64
 one year ago
Best ResponseYou've already chosen the best response.3yeah :) so my faux pas actually worked in my favor the first time so the point (1,4), assuming m=1 should be 14+7/sqrt(2) = 4/sqrt(2) = 2sqrt(2)

amistre64
 one year ago
Best ResponseYou've already chosen the best response.3and that is what we worked so hard to determine the first go around lol

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0where did u get the sq.rt of 2 frm

amistre64
 one year ago
Best ResponseYou've already chosen the best response.3sqrt(a^2+b^2) sqrt(m^2+1) , assumed m=1 sqrt(2) as a divisor 1/sqrt(2) .... rationalize the denominator (just multiply it all by sqrt(2)/sqrt(2) ) sqrt(2)/2 well, 4/2 = 2 sooo that reduces to 2s qrt(2)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0o yea I see.. forget about the sq.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so were finish with this question?

amistre64
 one year ago
Best ResponseYou've already chosen the best response.3all there is to it is plugging in our known values and leaving the rest to the imagination

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok but what about the other point (2,1)

amistre64
 one year ago
Best ResponseYou've already chosen the best response.3\[\frac{mx_0y_0+m+6}{\sqrt{m^2+1}}\] \[\frac{2m1+m+6}{\sqrt{m^2+1}}\] \[\frac{m+5}{\sqrt{m^2+1}}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0is that another equation that we can use to find distance

amistre64
 one year ago
Best ResponseYou've already chosen the best response.3that is the formula you presented to start with

amistre64
 one year ago
Best ResponseYou've already chosen the best response.3all i did was determine what A B and C were, and then its just a matter of plugging in the point values

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok I will have to look this through back when I'm fully awake to understand everything ..thanks very much
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