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  • The reflection of the point in the line <img alt="5 x+y+6=0" src="https://entrancecorner.oncodecogs.com/gif

The reflection of the point (4,-13) in the line 5 x+y+6=0 is

Option: 1

(-1,-14)


Option: 2

(3,4)


Option: 3

(1,2)


Option: 4

\quad(-4,13)


Answers (1)

best_answer

Let Q(a, b) be the reflection of  P(4,-13) in the line 5 x+y+6=0 . Then the point

R\left(\frac{a+4}{2}, \frac{b-13}{2}\right) \text { lies on } 5 x+y+6=0 \quad

\therefore \quad 5\left(\frac{a+4}{2}\right)+\left(\frac{b-13}{2}\right)+6=0 \quad \Rightarrow 5 a+b+19=0                ....(i)

Also P Q is perpendicular to 5 x+y+6=0.

Therefore \left(\frac{b+13}{a-4}\right) \times\left(\frac{-5}{1}\right) \Rightarrow a-5 b-69=0                                       ....(ii)

Solving (i) and (ii), we get

a=-1, b=-14

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mansi

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