Question
If the points $$A\left( {1,\,4} \right)$$ and $$B$$ are symmetrical about the tangent to the circle $${x^2} + {y^2} - x + y = 0$$ at the origin then coordinates of $$B$$ are :
A.
$$\left( {1,\,2} \right)$$
B.
$$\left( {\sqrt 2 ,\,1} \right)$$
C.
$$\left( {4,\,1} \right)$$
D.
none of these
Answer :
$$\left( {4,\,1} \right)$$
Solution :
The tangent at the origin is $$y - x = 0.\,B$$ is the image of $$A\left( {1,\,4} \right)$$ by this line.