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anonymous

  • 4 years ago

Find the point on the line y=x+1 that is closest to the point (4,1).

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  1. anonymous
    • 4 years ago
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    Do I need to substitute the 4 in place of x and the 1 in place of y? I am not sure how or where to start.

  2. Rogue
    • 4 years ago
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    I'll give you a hint. When the point on the line y = x + 1 that is closest to (4,1) is connected to (4,1), the line that is formed is perpendicular to y = x + 1.

  3. anonymous
    • 4 years ago
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    so the ending equation would be 1=4+1

  4. anonymous
    • 4 years ago
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    or would it be a negative

  5. Rogue
    • 4 years ago
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    Uhm, no. First find the line of the perpendicular line that crosses the point (4,1). The slope of a line perpendicular to to another line would be the negative reciprocal of the other line. The slope of y = x + 1 is 1. The slope of the perpendicular line should be -1. Put together the information you have to get the equation of the perpendicular line. m = -1, passes (4,1) y = -1(x - 4) + 1 = 5 - x Now the perpendicular line intersects the original line, so set the two lines equal. y = 5 - x y = x + 1 5 - x = x + 1 x = 2 At x = 2, y = 3. So the closest point is (2,3).

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