The perpendicular bisector of line segment joining the points P(1,4) and Q(k, 3) has y -intercept -4 . Then a possible value of k among the following is

Step-by-step solution

Let L R M is the perpendicular bisector of P Q at R [ . Slope of line passing through (x₁, y₁ ) and . (x₂, y₂ ) is y₂-y₁ x₂-x₁ ] aligned R & = ( 1+k 2 , 4+3 2 ) R & = ( k+1 2 , 7 2 ) aligned array c mid-point of line with end points (x₁, y₁ ), (x₂, y₂ ) = ( x₁+x₂ 2 , y₁+y₂ 2 ) array Also slope of P Q= 3-4 k-1 m_ P Q = -1 k-1 P Q and L M are perpendicular to each other. m_ L M = -1 m_ P Q = -1 -1 / k-1 m_ L M =k-1 Equation of L M which has slope (k-1) has Y -intercept -4 Equation of L M: y=(k-1) x-4 ...(i) Since, Eq