If the image of ( - 7 5 , - 6 5 ) in a line is (1, 2), then the equation of the line is

Question

If the image of $(- \frac{7}{5}, - \frac{6}{5})$ in a line is (1, 2), then the equation of the line is

Smart Achievers · Accepted Answer

(3)

$The required line is perpendicular bisector of the$ $line segment joining the two points.$

$Equation of line joining$ $(- \frac{7}{5}, - \frac{6}{5})$ $and$ $(1, 2)$ $is$

$\frac{y - 2}{x - 1} = \frac{\frac{- 6}{5} - 2}{\frac{- 7}{5} - 1}$ $\Rightarrow$ $4 x - 3 y + 2 = 0$

$A line perpendicular to this line is$ $3 x + 4 y + k = 0$ ...(i)

$Also, line (i) passes through the midpoint of$ $(- \frac{7}{5}, - \frac{6}{5})$ $and$ $(1, 2),$ $i.e.,$ $(\frac{- 1}{5}, \frac{2}{5})$

$∴$ $3 (- \frac{1}{5}) + 4 (\frac{2}{5}) + k = 0$ $\Rightarrow$ $k = - 1$

$So, the required line is$ $3 x + 4 y - 1 = 0$

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