The Perpendicular Bisector Of The Line Segment Joining P (1, 4) And Q (k, 3) Has Y−intercept − 4. Then A Possible Value Of K Is?
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An equation for a perpendicular bisector is developed here. It is
(y - (y1+y2)/2) = (x1 - x2)/(y2 - y1)(x - (x1+x2)/2)
Substituting the given point values, we have
(y - (4+3)/2) = (1-k)/(3-4)(x - (1+k)/2)
Substituting the given intercept values (0, -4) we have
-4 - 7/2 = (1-k)(1+k)/2
-15 = 1 - k^2 (multiply both sides by 2)
16 = k^2 (subtract 1 from both sides, then multiply by -1)
±4 = k (square root of both sides)
(y - (y1+y2)/2) = (x1 - x2)/(y2 - y1)(x - (x1+x2)/2)
Substituting the given point values, we have
(y - (4+3)/2) = (1-k)/(3-4)(x - (1+k)/2)
Substituting the given intercept values (0, -4) we have
-4 - 7/2 = (1-k)(1+k)/2
-15 = 1 - k^2 (multiply both sides by 2)
16 = k^2 (subtract 1 from both sides, then multiply by -1)
±4 = k (square root of both sides)
The variable k could be either -4 or +4.
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