Question

23.Point P(x, 4) lies on the line segment joining the points A(-5,8) and B(4, -10). Find
the ratio in which point P divides the line segment AB. Also find the value of x.

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Answer 1

Step-by-step explanation:

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Answer 2

Given : Point P ( x , 4)  lies on the line segment joining the points A(-5,8) and B(4, -10).

To Find :  Ratio in which it divides the line segment

value of x

Solution:

Let say Point P ( x , 4)  divided the line segment joining the points A(-5,8) and B(4, -10)  in ratio   k : 1

then  x = (4k  - 5)/(k + 1)   and 4  = ( -10k  + 8 )/(k + 1)

4  = ( -10k  + 8 )/(k + 1)

=> 2 = (-5k + 4)/(k + 1)

=> 2k + 2 = - 5k + 4

=> 7k = 2

=> k = 2/7

=> k  : 1  = 2 : 7

x = (4k  - 5)/(k + 1)

=> x =  ( 4 (2/7) - 5) / ( 2/7  + 1)

=> x = ( 8 - 35) / ( 2 + 7)

=> x = -27/9

=> x = - 3

Point P ( x , 4)  divided the line segment joining the points A(-5,8) and B(4, -10)  in ratio   2 : 7

and  x = - 3

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