anonymous
  • anonymous
Find the distance between the point (5,6), and the line
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
1 Attachment
ganeshie8
  • ganeshie8
|dw:1378833963374:dw|
ganeshie8
  • ganeshie8
we're supposed to find the perpendicular distance from (5, 6) to that line

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ganeshie8
  • ganeshie8
|dw:1378834062341:dw|
ganeshie8
  • ganeshie8
If we can some how find that intersecting point, we can use distance formula to find the distance
ganeshie8
  • ganeshie8
before finding the intersecting point, lets find the equation for that perpendicular line, any clue how to find the equation for that line ?
anonymous
  • anonymous
you add 3 on both sides?
ganeshie8
  • ganeshie8
hmm we're trying to find the equation of the perpendicular line.
anonymous
  • anonymous
sorry.. idk how to do this at all :(
ganeshie8
  • ganeshie8
obserrve that its going thru (5, 6), since its perpendicular to 2x-3y+2 = 0, its slope wud be, -3/2 so the equation of that line wud be :- y = -3/2x + 13.5 or, 2y = -3x + 27 3x+2y -27 = 0
ganeshie8
  • ganeshie8
its okay :) forget everything i told u so far, we will simply use a formula and find the distance ok :)
anonymous
  • anonymous
okay :) so whats the formula?
ganeshie8
  • ganeshie8
here is the formula :- \(\large \frac{|Ax_1 + By_1 + C|}{\sqrt{A^2+B^2}}\)
ganeshie8
  • ganeshie8
point = (5,6) so, \(x_1=5\) ,\(y_1=6\)
ganeshie8
  • ganeshie8
line : 2x-3y+2 = 0 so, \(A = 2, B = -3, C = 2\)
ganeshie8
  • ganeshie8
plug in, and simplify :)
anonymous
  • anonymous
okay thanks :) how would i plug it in the caculator?
ganeshie8
  • ganeshie8
let me show you how to plug the numbers :)
anonymous
  • anonymous
okay :)
ganeshie8
  • ganeshie8
we have this formula :- \(\large \frac{|Ax_1 + By_1 + C|}{\sqrt{A^2+B^2}}\) plug the above numbers, \(\large \frac{|2 \times 5 + -3 \times 6 + 2|}{\sqrt{2^2+(-3)^2}}\)
ganeshie8
  • ganeshie8
\(\large \frac{|10-18+2|}{\sqrt{4+9}}\)
ganeshie8
  • ganeshie8
\(\large \frac{6}{\sqrt{13}}\)
ganeshie8
  • ganeshie8
\( 1.66\)
anonymous
  • anonymous
thank you for going through it by steps. now i got it :) but the answer choices are a. 6 c. b. d. 5
anonymous
  • anonymous
6, square root of 13, 6 square root of 13 over 13 or 5 square root of 2
anonymous
  • anonymous
since you said 1.66, it would be 6?
ganeshie8
  • ganeshie8
noo, they want the exact answer
ganeshie8
  • ganeshie8
we got \(\large \frac{6}{\sqrt{13}}\)
ganeshie8
  • ganeshie8
rationalize th edenominator
anonymous
  • anonymous
oh so its 6 over square root of 13
anonymous
  • anonymous
:)
ganeshie8
  • ganeshie8
\(\large \frac{6}{\sqrt{13}} \times \frac{\sqrt{13}}{\sqrt{13}}\)
ganeshie8
  • ganeshie8
\(\large \frac{6\sqrt{13}}{13} \)
ganeshie8
  • ganeshie8
that should be our final answer :)
anonymous
  • anonymous
ohhhh okay i got 6! haha
ganeshie8
  • ganeshie8
lol, wat do u mean u got 6 ?
ganeshie8
  • ganeshie8
|dw:1378836090577:dw|
anonymous
  • anonymous
ohhh i thought you wanted me to put that in my caculator lol. oh now i see what you did xD
ganeshie8
  • ganeshie8
good :)

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