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Find the constant k k so that the perpendicular bisector of the line segment with end points (k,0) (k , 0) and (4,6) (4 , 6) has a slope of −3-3.

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Full solution

Q. Find the constant k k so that the perpendicular bisector of the line segment with end points (k,0) (k , 0) and (4,6) (4 , 6) has a slope of −3-3.
  1. Calculate Midpoint: Calculate the midpoint of the line segment with endpoints (k,0)(k, 0) and (4,6)(4, 6).
  2. Determine Slope: Determine the slope of the line segment.
  3. Use Perpendicular Bisector Property: Use the property that the slope of the perpendicular bisector is the negative reciprocal of the slope of the line segment.
  4. Solve for kk: Solve for kk.

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