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

x + y = 2

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8 x + y = 9

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7 x - y = 6

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none of these

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Solution

The correct option is C $7 x - y = 6$
The locus of the point $(h, k)$ can be given by
$\frac{x_{2} - h}{2} = \frac{y_{2} - k}{- 1} = \frac{- (2 h - k - 1)}{5}$
This implies that
$x_{2} = \frac{- 3 h + 4 k + 4}{5}$
$y_{2} = \frac{4 h + 3 k - 2}{5}$
Since the point is on the line $y = x$ , we get
$\frac{- 3 h + 4 k + 4}{5} = \frac{4 h + 3 k - 2}{5}$
$7 h - k = 6$
Replacing $(h, k)$ by $(x, y)$ we get
$7 x - y = 6$

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Similar questions

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

x^{2} + y^{2} - 2 y - 9 = 0

4 x + y = 1

A (2, - 7)

B C

3 x - 4 y + 1 = 0

B

A B = A C

A C

x - y = 7

x + 4 y = 2

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