Question

P
6. The point P divides the line-segment joining the points
A(x,y) and B(x2, yy) in the ratio m:n. If P lies on the
line ax + by + C = 0, prove that,
axi + by, +C
ax₂ +by+c
m
n​

Answer 1

Answer:

Given that point P(x,y) divides the line segment joining A(x

1

y

1

) B(x

2

y

2

) in the ratio m

1

:m

2

then the coordinates of P can be obtained using the section formula.

( Diagram )

Using section formula we can write :

⇒(x,y)≡(

m

2

m

2

m

1

x

2

+m

2

x

1

,

m

1

+m

2

m

1

y

2

+m

2

y

2

)

Hence, the answer is (

m

2

m

2

m

1

x

2

+m

2

x

1

,

m

1

+m

2

m

1

y

2

+m

2

y

2

).

solution