Math-Calculus

Find the point on the line -2x + 4y + 3 =0 which is closest to the point (-2,1). Note: I have been struggling on this for hours!

asked by Jacob
  1. For hours ???

    Slope of the given line is 1/2
    so the slope of the line through (-2,1) and perpendicular to it must be -2
    equation of that perp.
    y = -2x + b, with (-2,1) lying on it, thus ...
    1 = -2(-2) + b
    -3 = b

    y = -2x - 3
    solve the two equations to get the required point
    -2x + 4y + 3 = 0
    -2x + 4(-2x-3) + 3 = 0
    -2x -8x - 12 + 3 = 0
    -10x = 9
    x = -9/10
    sub that back into y = -2x-3
    y = -2(-9/10) - 3 = -6/5

    the point is (-9/10 , -6/5)

    posted by Reiny
  2. Thank you very much Reiny for this wonderful explanation. I am not the brightest bulb and yes 2 hours to be precise.

    posted by Jacob

Respond to this Question

First Name

Your Response

Similar Questions

  1. Calculus-Applied Optimization Problem:

    Find the point on the line 6x + 3y-3 =0 which is closest to the point (3,1). Note: Your answer should be a point in the xy-plane, and as such will be of the form (x-coordinate,y-coordinate)
  2. calculus

    Ola, I'm not understanding this question, any assistance? Thank you very much. Find the distance of the line y = 2x + 6 from the circle x^2 + y^2 = 0.5 Find the point of the line that is closest to the circle. [Hint: a point on
  3. Math

    For the given point and line, find by projection the point on the line that is closest to the given point and use perp to find the distance from the point to the line. P (3,-5) line: x = (2,-4)+t(3,-4)
  4. Calculus

    Find the point on the line 6x + y = 9 that is closest to the point (-3,1). Solution: We need to minimize the function d =
  5. calculus help amigos

    Find the point on the line 5x+5y+7=0 which is closest to the point (3,−4)
  6. calculus

    Find the point on the line 2x+4y+7=0 which is closest to the point (4,−3).
  7. Calculus

    Find the point on the line 2x+7y-6=0 which is closest to the point (-5,5.
  8. Calculus

    Find the point on the line -3 x + y + 4 =0 which is closest to the point ( -5, 0 ).
  9. Calculus

    Find the point on the line 4x+3y-4=0 which is closest to the point (5,2)
  10. calculus

    Find the point on the line 4x+2y+5=0 which is closest to the point (-2,-1)

More Similar Questions