JEE Mains · Maths · STD 11 - 9. straight line
If the perpendicular bisector of the line segment joining the points \(P (1,4)\) and \(Q ( k , 3)\) has \(y\)- intercept equal to \(-4,\) then a value of \(k\) is
- A \(\sqrt{15}\)
- B \(-2\)
- C \(\sqrt{14}\)
- D \(-4\)
Answer & Solution
Correct Answer
(D) \(-4\)
Step-by-step Solution
Detailed explanation
Slope \(= m =\frac{1}{1- k }\) Equation of \(\perp^{ r }\) bisector is \(y+4=(k-1)(x-0)\) \(\Rightarrow y +4= x ( k -1)\) \(\Rightarrow \frac{7}{2}+4=\frac{ k +1}{2}( k -1)\) \(\Rightarrow \frac{15}{2}=\frac{ k ^{2}-1}{2} \Rightarrow k ^{2}=16 \Rightarrow k =4,-4\)
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