Find the ratio in which (-1,y) divides the line joining (-3,10) and (6,-8).
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x1 = - 3
x2 = 6
y1 = 10
y2 = - 8
x = - 1
=> (m1 x2 + m2 x1) / ( m1 + m2) = - 1
[ sectional formula]
=> [ m1 × 6 + m2 × (-3)] = - 1 ( m1 + m2)
=> 6 m1 - 3m2 = - m1 - m2
=> 6 m1 + m1 = 3 m2 - m2
=> 7 m1 = 2 m2
=> m1 / m2 = 2 / 7
=> m1 : m2 = 2 : 7
Required ratio = 2 : 7
Now,
y = (m1 y2 + m2 y1) / (m1 + m2)
=> y = ( 2 × - 8 + 7 × 10) / ( 2 + 7)
=> y = ( - 16 +70) / 9
=> y = 54 / 9
=> y = 6
x2 = 6
y1 = 10
y2 = - 8
x = - 1
=> (m1 x2 + m2 x1) / ( m1 + m2) = - 1
[ sectional formula]
=> [ m1 × 6 + m2 × (-3)] = - 1 ( m1 + m2)
=> 6 m1 - 3m2 = - m1 - m2
=> 6 m1 + m1 = 3 m2 - m2
=> 7 m1 = 2 m2
=> m1 / m2 = 2 / 7
=> m1 : m2 = 2 : 7
Required ratio = 2 : 7
Now,
y = (m1 y2 + m2 y1) / (m1 + m2)
=> y = ( 2 × - 8 + 7 × 10) / ( 2 + 7)
=> y = ( - 16 +70) / 9
=> y = 54 / 9
=> y = 6
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