math

Find the exact value of the shortest distance from the origin to each line. y=x-4 is the equation of the line. When i do the problem I keep on getting 0 but that's not the answer!!! please help me.

  1. 👍 0
  2. 👎 0
  3. 👁 73
  1. y = x-4 does not go through the origin
    to find the shortest distance from a point to a line find the line perpendicular to the given line and through the point first.
    slope of perpendicular line = -1/original slope = -1/1 = -1
    so
    y = -x is our line (b = 0 because it goes through origin)
    Now where does that line hit the original one?
    y = x - 4
    y = -x
    so
    -x = x - 4
    2 x = 4
    x = 2
    then y = -2
    Now we have two points
    (0,0) and (2,-2)
    what is the distance between them?
    d = sqrt (2^2+(-2)^2) = sqrt 8 = 2 sqrt 2

    1. 👍 0
    2. 👎 0
    posted by Damon
  2. ok, but if i were dealing with the formula ... *absolute value*Ax+By+C/over -> *square root* A^2 +B^2

    1. 👍 0
    2. 👎 0
    posted by Allison
  3. Well, interesting and limited to finding distance only from origin but if you insist:
    y = x - 4
    write in form
    1 x - 1 y - 4 =0
    A = 1
    B = -1
    C = -4
    |A+B+C|=4
    sqrt(A^2+B^2) = sqrt 2
    4/sqrt2 = (4 sqrt 2)/ 2 = 2 sqrt 2

    1. 👍 0
    2. 👎 0
    posted by Damon
  4. its the |A+B+C|=4.. because our P.O.I was (2,-2), therefore A=1(2) + B=-1(-2) and C=-4....that makes 2+2-4.. that's 0

    1. 👍 0
    2. 👎 0
    posted by Allison
  5. Now wait a minute.
    If you are trying to find the distance ,d, between points P (Xp, Yp) and Q (Xq ,Yq)
    distance in x = (Xq-Xp)
    distance in y = (Yq-Yp)
    d = hypotenuse = sqrt [(Xq-Xp)^2 +(Yq-Yp)^2 ]
    here our two points are
    (0,0) and (2,-2)
    so
    d = sqrt [(2-0)^2 + (-2-0)^2 ]
    = sqrt (4+4)
    =sqrt(8)
    = 2 sqrt 2

    1. 👍 0
    2. 👎 0
    posted by Damon
  6. Are you sure your formula is not just |A+B+C|/sqrt(A^2+B^2) ?
    It does not make sense to find the (2,-2) point and then go to the trouble of using your formula. I have never seen (or needed) this formula.

    1. 👍 0
    2. 👎 0
    posted by Damon
  7. Given the line Ax + By + C = 0 and a point (a,b) not on that line, then the shortest distance from the point to the line is
    |Aa + Bb + C|/√(A^2 + B^2)

    the point is (0,0) and x-y-4=0
    so here distance =|0 + 0 - 4|/√(1+1) = 4/√2 = 2√2 as Damon found for you

    1. 👍 0
    2. 👎 0
    posted by Reiny
  8. hel p

    1. 👍 0
    2. 👎 0
    posted by cassidy

Respond to this Question

First Name

Your Response

Similar Questions

  1. Math

    How do you: Find the shortest distance, to two decimal places from the origin to the line x - 2y = - 8 without using the formula. Finding the shortest distance, to two decimal places, from the point P ( 7,5) to the line 2x+3y =

    asked by Jack on May 11, 2007
  2. Mathematics

    Determine the shortest distance from a house situated at the origin to a road that is represented by the line 3y+x+18=0

    asked by Mokotedi on March 8, 2011
  3. Linear Algebra

    Let L be the line with parametric equations x = 1−2t y = 3+3t z = −1−3t Find the shortest distance d from the point P0=(1, −4, −2) to L, and the point Q on L that is closest to P0. Use the square root symbol '√' where

    asked by Ramit Rana on November 29, 2016
  4. Linear Algebra

    Let L1 be the line passing through the point P1=(9, −1, 15) with direction vector →d1=[−2, −1, −3]T, and let L2 be the line passing through the point P2=(9, 4, 8) with direction vector →d2=[−2, −1, −1]T. Find the

    asked by Garrett on November 11, 2018
  5. Linear algebra

    Let L1 be the line passing through the point P1=(−1, −1, 8) with direction vector →d1=[1, 0, −3], and let L2 be the line passing through the point P2=(7, −11, 14) with direction vector →d2=[1, 2, −3]. Find the

    asked by sara on March 18, 2017
  6. Linear Algebra

    Let L be the line with parametric equations x = 1−2t y = 3+3t z = −1−3t Find the shortest distance d from the point P0=(1, −4, −2) to L, and the point Q on L that is closest to P0. Use the square root symbol '√' where

    asked by Ramit Rana on November 29, 2016
  7. math

    A straight line is the shortest distance between two points. In a triangle, the sum of two sides of the triangle is greater than the third side. Also, a perpendicular drawn from a point to a line is the shortest distance from the

    asked by peter on May 15, 2014
  8. Algebra

    can anybody help me with this question please? Let L be the line passing through the point P=(5, −5, 3) with direction vector →d=[1, −3, −2]T. Find the shortest distance d from the point

    asked by shana on March 1, 2017
  9. Linear Algebra

    Let L be the line with parametric equations x = 2+3t y = 3−2t z = 2+t Find the shortest distance d from the point P0=(−5, 1, −4) to L, and the point Q on L that is closest to P0. Use the square root symbol '√' where needed

    asked by Angel on November 26, 2017
  10. Algebra

    can somebody please help me with this question I've spent more than 3 hours on this, still nothing Let L1 be the line passing through the point P1=(2, −4, −6) with direction vector →d1=[1, 0, 2]T, and let L2 be the line

    asked by sara on March 18, 2017

More Similar Questions