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The harmonic conjugate of (7, 5) with respect to the points (4 , 2) and (9,7) is

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$(19, 17)$

$(1, 4)$

$(\frac{7}{6}, \frac{8}{6})$

$(- 4, - 1)$

answer is D.

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Detailed Solution

$P (7, 5), A (4, 2), B (9, 7)$ P divided $\bar{A B}$ in the ratio $4 - 7 : 7 - 9 = - 3 : - 2 = 3 : 2$

Harmonic conjugate of P divides $\bar{A B}$ in the ratio $- 3 : 2$

Harmonic conjugate of P is $\frac{- 3 B + 2 A}{- 3 + 2} = \frac{(- 27, - 21) + (8, 4)}{- 1} = (19, 17)$

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