Question

The harmonic conjugate of (7.5) with respect to the points (4,2) and (9.7) is
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Answer 1

Answer:

The ratio in which (4,-2) divides |AB| is

(2-4):(4-1) = -2 : 3

∴ The point which divides AB in the ratio -2 : 3 is

P(x,y)=[ {-2(7) - 3(2)}/3-2 , {-2(1) - 3(-4)}/3-2]

∴ P(x,y) = (-20,10

Answer 2

Answer:

The required harmonic conjugate is (19,17).

Step-by-step explanation:

The correct question is-"The harmonic conjugate of (7,5) with respect to the points (4,2) and (9,7) is?"

The given points are (4,2) and (9,7)

Let us assume that the point (7,5) divides the join of (4,2) and (9,7) in the ratio a:b.Therefore we can write

$7=\frac{a(9)+b(4)}{a+b} = > 7a+7b=9a+4b\\= > 2a-3b=0\\= > \frac{a}{b}=\frac{3}{2}$

The point divides the join in the ratio 3:2 and hence the harmonic conjugate of the point will divide (4,2) and (9,7) in the ratio -3:2.

Therefore the harmonic conjugate is

$P(x,y)=(\frac{-3(9)+2(4)}{-3+2} ,\frac{-3(7)+2(2)}{-3+2} )\\=(19,17)$

Therefore,

The required harmonic conjugate is (19,17).

#SPJ2

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