Question

Find the ratio in which (-1,y) divides the line joining (-3,10) and (6,-8).

Answer 1

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