A) \[(-1,-14)\]
B) (3 ,4)
C) (1, 2)
D) (- 4, 13)
Correct Answer: A
Solution :
Let \[Q(a,b)\] be the reflection of \[P(4,-13)\] in the line \[5x+y+6=0\]. Then the mid-point \[R\text{ }\left( \frac{a+4}{2},\frac{b-13}{2} \right)\] lies on \[5x+y+6=0\]. \ \[5\left( \frac{a+4}{2} \right)+\frac{b-13}{2}+6=0\Rightarrow 5a+b+19=0\] ......(i) Also \[PQ\]is perpendicular to \[5x+y+6=0\]. Therefore \[\frac{b+13}{a-4}\times \left( -\frac{5}{1} \right)=-1\Rightarrow a-5b-69=0\] .....(ii) Solving (i) and (ii), we get\[a=-1,\,\,b=-14\].You need to login to perform this action.
You will be redirected in
3 sec