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…

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
  1. $\left(\frac{-1}{5}, \frac{13}{5}\right)$
  2. $\left(\frac{-7}{5}, \frac{9}{5}\right)$
  3. $\left(\frac{7}{5}, \frac{-9}{5}\right)$
  4. $\left(\frac{-7}{5}, \frac{-9}{5}\right)$

Solution


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 $M\left(-\frac{1}{5}, \frac{13}{5}\right)$

Asked in: AP EAMCET 2004

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