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Find k, given that (2,k) is equidistant from (3,7) and (9,1).

The answer is : k=0

How do I solve this problem?

  • Algebra -

    The slope of the line segment joining (3,7) and (9,1) is -6/6 = -1.

    Any point equidistant from those two points will lie on the perpendicular bisector of that line segment.

    So, we want the line with slope=1, through (6,4), the midpoint of the segment.

    y-4 = 1(x-6)
    Now, we plug in (2,k) to get
    k-4 = 2-6
    k = 0

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