Question

find the hormonic conjugates of point R(2,4) with respect to the points P(2,2) and (2,5)​

Answer 1

Answer:

ANSWER

Let (5,1) divides the line joining P & Q

in λ:1

so, X−coordinate of R=

λ+1

6λ+2

Y−coordinate of R=

λ+1

−2λ+10

⇒

λ+1

6λ+2

=5

⇒ 6λ+2=5λ+5

λ=3

so, we need to find a point which divide P and Q in 3:1

∴ R

X

=

−3+1

(−3)(6)+2

=−16/−2=8

R

y

=

−3+1

(−3)(−2)+10

=16/−2=−8

∴ harmonic conjugate of

(5,1) is (8,−8)

solution

Answer 2

Answer:

Step-by-step explanation:

we have P(2,2) and Q(2,5)

Let R divided PQ in the ratio k:1,so we can write as

(4,2)=[(2k+2)/(k+1),(5k+2)/(k+1)]

so we get; k=2

due to external division we can use formula (MX2-NX1)/M+N,(MY2-NY1)/M+N

final ans is (a,b)=( 2.2-1.2/2-1,5.2-1.2/2-1)

(a,b)=(2,8) thank you