First slide

Equation of line in Straight lines

Question

The equation of the line AB is y = x. If A and B lie on the same side of the line mirror 2x - y = 1, then the equation of the image of AB, is

Moderate

A

$x + y - 2 = 0$
B

$8 x + y - 9 = 0$
C

$7 x - y - 6 = 0$
D

none of these

Solution

The required line is the line passing through the intersection of two lines and the image of a point on the line y = x in the line minor 2x - y ~· l.
$\frac{x - 0}{2} = \frac{y - 0}{- 1} = - 2 (\frac{2 \times 0 - 0 - 0 - 1}{4 + 1})$
$\Rightarrow x = \frac{4}{5}, y = \frac{- 2}{5}$
Thus, the required line passes through (1, 1) and $(\frac{4}{5}, \frac{- 2}{5})$
So, its equation is
$\begin{array}{l} y - 1 = \frac{^{2} - 1}{4} (x - 1) \\ y - 1 = 7 (x - 1) \Rightarrow 7 x - y - 6 = 0 \end{array}$

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