Math

Find the point on the line 7x+1y−2=0 which is closest to the point (−1,−3).

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  1. draw a line perpendicular to the first one
    what is its slope?
    original line:
    y = -7 x + 2 so the original slope is -7

    slope of perpendicular = -1/-7 = 1/7
    now make that perpendicular go through (-1,-3)
    -3 = (1/7)(-1) + b
    -3 +1/7 = b
    b = -20/7
    so our line is
    y = (1/7)x -20/7
    where does that hit our original line
    -7x+2 = (1/7)x -20/7
    -49 x + 14 = x -20
    50 x = -6
    x = -3/25
    y = -7(-3/25)+2=21/25+50/25 = 71/25

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