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If P (3,7) is a point on the line joining A (1,1) and B (6,16) then the harmonic conjugate Q of point P has the coordinates?

If P (3,7) is a point on the line joining A (1,1) and B (6,16) then the harmonic conjugate Q of point P has the coordinates?

Grade:12

1 Answers

Vikas TU
14149 Points
3 years ago
The harmonic conjugate is given by,
 suppose a point p divides a line segment joining two points a and b in the ratio m:n , then the harmonic conjugate will divide the same line in the ratio m:−n
A (1,1)
B (6,16)
P(3,7)
let the ratio in which P divides AB is 1:m
then,
⇒(m.1+6)(1+m)=3
⇒m+6=3+3m
m=3/2
Hence , P divides AB in ratio 2:3 
Now harmonic conjugate will divide AB in ratio 2:−3
Hence, let (h,k) be harmonic conjugateh=2.6−3.1 / 2−3 = 9/−1=−9
k=2.16−3.1 / 2−3=−29
(h,k) = (−9,−29) 

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