The reflection of the point (4,-13) about the line `5x+y+6=0` is `(-1,-14)` b. `(3,4)` c. `(0,-0)` d. `(1,2)`

Options

A. (1,-14)
B. (6,-15)
C. (-1,-14)
D. none of these

Answer

C

Explanation

Let `Q(x_(1),y_(1))` be the image of the point P(4,-13) in the line mirror `5x+y+6=0` . Then, the coordinates of Q are given by
`(x_(1)-4)/(5)=(y_(1)+13)/(1)=(-2(5xx4-13+6))/(5^(2)+1^(2))`
`implies (x_(1)-4)/(5)=(y_(1)-13)/(1)=1`
`implies x_(1)-4=-5 and y_(1)+13=-1`
`implies x_(1)=-1 and y_(1)=-14`
Hence, the image of the point P(4,-13) in the line mirror `5x+y+6=0` is (-1,-14).