Mam I could not get the ques I m not able to see ur answer - Maths -

Question

Mam I could not get the ques I m not able to see ur answer
properly A line is such that is segment b/w the lines 5x -
y + 4 = 0 and 3x + 4y - 4 = 0 is bisected at the point ( 1, 5) How
we will find its equation ???Pls explain memam !! Pls post
ur answer as soon as possible again !!!

Lalit Mehra · Accepted Answer

The given lines are 5x â€“ y + 4 = 0 (1) 3x + 4y â€“ 4 = 0 (2) Let the required line intersects the lines (1) and (2) at (x1, y1) and (x2, y2) respectively (x1, y1) lies on (1) $∴ 5 x_{1} - y_{1} + 4 = 0 \Rightarrow y_{1} = 5 x_{1} + 4$ (x2, y2) lies one (2) $∴ 3 x_{2} + 4 y_{2} - 4 = 0 \Rightarrow y_{2} = \frac{4 - 3 x_{2}}{4}$ Given, the segment between the lines is bisected at the point (1, 5) $∴ \frac{x_{1} + x_{2}}{2} = 1 \Rightarrow x_{1} + x_{2} = 2 (3) and \frac{y_{1} + y_{2}}{2} = 1 \Rightarrow \frac{5 x_{1} + 4 + \frac{4 - 3 x_{2}}{4}}{2} = 1 \Rightarrow 20 x_{1} - 3 x_{2} = 20 (4)$ Solving (3) and (4), we have $x_{1} = \frac{26}{23} and x_{2} = \frac{20}{23} W hen x_{1} = \frac{26}{23}, y_{1} = 5 (\frac{26}{23}) + 4 = \frac{222}{23} [∵ y_{1} = 5 x_{1} + 4]$ Equation of the straight line passing through (1, 5) and $(\frac{26}{23}, \frac{222}{23}) is$ $y - 5 \frac{\frac{222}{23} - 5}{\frac{26}{23} - 1} (x - 1) [∵ y - y_{1} = \frac{y_{2} - y_{1}}{x_{2} - x_{1}} (x - x_{1})]$ $\Rightarrow y - 5 = \frac{107}{3} (x - 1) \Rightarrow 3 y - 15 = 107 x - 107 \Rightarrow 107 x - 3 y - 92 = 0$ Thus, the equation of required line is 107x â€“ 3y â€“ 92 = 0

Mam.. I could not get the ques... I m not able to see ur answer properly.. A line is such that is segment b/w the lines 5x - y + 4 = 0 and 3x + 4y - 4 = 0 is bisected at the point ( 1, 5). How we will find its equation ???Pls explain memam !! Pls post ur answer as soon as possible again.... !!!