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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Answers
Step-by-step explanation:
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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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