AP EAMCET · Maths · Straight Lines
Suppose \(A, B\) are two points on \(2 x-y+3=0\) and \(P(1,2)\) is such that \(P A=P B\). Then, the mid-point of \(A B\) is
- A \(\left(\frac{-1}{5}, \frac{13}{5}\right)\)
- B \(\left(\frac{-7}{5}, \frac{9}{5}\right)\)
- C \(\left(\frac{7}{5}, \frac{-9}{5}\right)\)
- D \(\left(\frac{-7}{5}, \frac{-9}{5}\right)\)
Answer & Solution
Correct Answer
(A) \(\left(\frac{-1}{5}, \frac{13}{5}\right)\)
Step-by-step Solution
Detailed explanation
Therefore its slope is \(\left(-\frac{1}{2}\right)\). \(\therefore\) Equation of line \(P M\) is \[ y-2=-\frac{1}{2}(x-1) \] On solving Eqs. (i) and (ii), we get the mid-point of \(A B\) is \(M\left(-\frac{1}{5}, \frac{13}{5}\right)\).
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