Question

find the ratio in which P( 4, m) divides the line segment joining the points A(2,3) and B( 6 ,- 3 hence find M

Answer 1

Hey mate !!

Here's your answer !!

Let the ratio be k : 1

A = (2,3)

B = (6,-3)

P = (4,m)

Lets calculate the k first

Applying section formula:-

= k(6) + 1(2) / k + 1 = 4

= 6k + 2 / k + 1 = 4

= 6k + 2 = 4 ( k + 1 )

= 6k + 2 = 4k + 4

= 6k - 4k = 4 - 2

= 2k = 2

=> k = 2/2 = 1

Hence the ratio would be k:1 which is 1:1

Therefore P is the midpoint of this line.

Hence M can be calculated by mid point formula.

M = 3 + ( - 3 ) / 2

M = 3 - 3 / 2

M = 0 / 2 = 0

Hence M = 0 and Ratio is 1 : 1

Hope this helps !!

Cheers !!

Answer 2

Hiii friend,

LET POINT P DIVIDES THE LINE SEGMENT AB IN K:1.

Let,

K = m , 1 = n

A(2,3) , B(6,-3) , P(4,m)

THEREFORE,

COORDINATES OF POINT P = MX2+NX1/M+N , MY2+NY1/2.

= P(K×6 + 1×2 / K+1 ) , (K×-3+1×3/ K+1)

= P(6K + 2/K+1) , (-3K+3/K+1)

BUT THE COORDINATES OF POINT P IS P(4,M) .

THEREFORE,

6K+2/K-1 = 4

6K+2 = 4(K+1)

6K-2 = 4K + 4

6K-4K = 4-2

2K = 2

K = 2/2 = 1

Point P (4,0) Divides the line segment AB in 1:1

And,

-3K + 3 / K+1 = m.

-3×1 + 3 / 1+1 = m

-3 + 3/ 2= m

M = 0/2 = 0