Question

Harmonic conjugate of the point $C(5,1)$ with respect to the point $A(2,10)$ and $B(6,-2)$ is?

• A. $(8,-8)$
• B. $(-1,3)$
• C. $(6,-4)$
• D. $(2,5)$

Answer 1

Answer: (A)

$(8,-8)$

$A=(2,10),B=(6,-2),C=(5,1)$

Let it divides in $\lambda :1$

$\frac{2+6\lambda }{\lambda +1}=5$ and $\frac{-2+10\lambda }{\lambda +1}=1$

On solving we get $\lambda =3$

So, the required point is $[\frac{-2+6\times 3}{-3+1}$$,\frac{-2-10\times 3}{-3+1}]=(8,-8)$