Question

Find the ratio in which pl-4.6) divides
the line spining points A (-6, 10) and
B (3,-8) internally​

Answer 1

Question:

Find the ratio in which P(-4.6) divides the line joining the points A(-6, 10) and B(3,-8) internally .

Answer:

2:7

Note:

• If the point P(x,y) divides the line joining the points A(x1,y1) and B(x2,y2) internally in the ratio m:n , then the co-ordinates of the point P will be ;

x = (m•x2 + n•x1)/(m + n)

y = (m•y2 + n•y1)/(m + n)

• If the point P(x,y) divides the line joining the points A(x1,y1) and B(x2,y2) externally in the ratio m:n , then the co-ordinates of the point P will be ;

x = (m•x2 - n•x1)/(m - n)

y = (m•y2 - n•y1)/(m - n)

Solution:

Let the P(-4.6) divides the line joining the points A(-6, 10) and B(3,-8) internally in the ratio m:n .

Thus,

Clearly we have ;

x = -4

y = 6

x1 = -6

y1 = 10

x2 = 3

y2 = -8

Thus,

The x-coordinates of point P will be given as;

=> x = (m•x2 + n•x1)/(m + n)

=> -4 = {m•3 + n•(-6)}/(m + n)

=> -4•(m+n) = 3m - 6n

=> -4m - 4n = 3m - 6n

=> 6n - 4n = 3m + 4m

=> 2n = 7m

=> n/m = 7/2

=> m/n = 2/7

=> m:n = 2:7

Hence,

The required ratio is 2:7 .

Answer 2

QUESTION :-

Find the ratio in which point p (-4,6) divides line joining points A(-6,10) B(3,-8) internally ?

ANSWER :-

2:7

STEP BY STEP EXPLAINATION:-

FORMULA TO BE USED :-

$(p,q) = ( \frac{lb + ma}{l + m} , \: \frac{ld + mc}{l + m} )$

SOLUTION :-

GIVEN DATA :-

p = -4 , q = 6 , a = -6 , b = 3 , c = 10 , d = -8 , l:m = ?

PROCEDURE :-

$(p,q) = ( \frac{lb + ma}{l + m} , \: \frac{ld + mc}{l + m} ) \\ ( - 4,6) = ( \frac{l(3) + m( - 6)}{l + m} , \: \frac{l( - 8)+ m( - 10)}{l + m} ) \\ considering \: x \: coeffcient \\ - 4(l + m) = 3l - 6m \\ - 4l - 4m \: = 3l - 6m \\ 7l = 2m \\ \frac{l}{m} = \frac{2}{7}$

l:m = 2:7

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