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 the m

Answer 1

take it and solve your ques.

Answer 2

Let P(4,m) divide AB internally

in the ratio k:1 .

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Section Formula :

The coordinates of the P(x,y)

Which divides the line segment

joining the points A(x1,y1) and

B(x2 , y2) internally in the ratio

m:n are

x = ( mx2 + nx1 )/(m+n) ,

y = ( my2 + ny1 )/( m + n )

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Here ,

A(x1,y1) = (2,3)

B(x2 ,y2) = ( 6,-3)

P(x,y) = ( 4,m )

m:n = k:1

Now ,

x = (k×6 + 1×2)/(k+1) = 4

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

=> 6k + 2 = 4k + 4

=> 6k - 4k = 4 - 2

=> 2k = 2

=> k = 2/2 = 1 ----( 1 )

ii ) y = [ k×(-3)+1×3]/(k+1) = m

=> (-3k+3)/(k+1) = m

=>( -3 + 3 )/( 1 + 1 ) = m [ from (1)]

=> 0 = m

Therefore ,

m = 0