Question

find the ratio in which p ( 4,m) divide the line sigement joining the points A( 2, 3) and B ( 6 - 3 ) hence find m

Answer 1

We know that,

x = (m1 x2 + m2 x1) / (m1 + m2)

Put the values,

4 = (m1×6 + m2 × 3) / m1 + m2

=> 4m1 + 4m2 = 6m1 + 3m2

=> 4m2 - 3m2 = 6m1 - 4m1

=> m2 = 2 m1

=> m1 / m2 = 1 /2

=> m1 : m2 = 1 : 2

Now,

Y = (m1 y2 + m2 y1) / (m1 +m2)

=> m = ( 1 × 3 + 2 × 3) / (1 +2)

=> m = 9 / 3

=> m = 3

Answer 2

We know that,

x = (m1 x2 + m2 x1) / (m1 + m2)

Put the values,

4 = (m1×6 + m2 × 3) / m1 + m2

=> 4m1 + 4m2 = 6m1 + 3m2

=> 4m2 - 3m2 = 6m1 - 4m1

=> m2 = 2 m1

=> m1 / m2 = 1 /2

=> m1 : m2 = 1 : 2

Now,

Y = (m1 y2 + m2 y1) / (m1 +m2)

=> m = ( 1 × 3 + 2 × 3) / (1 +2)

=> m = 9 / 3

=> m = 3

hope it helped ⚡