Question

find the coordinate of the point which divides the line-segment joining the points (-1,4) and (0,-3) in the ratio 1:4 internally

Answer 1

Let P (x,y) be the required point.

P divides AB internally in the ratio 1:4.

Here, m₁ = 1, m₂ = 4 , x₁ = -1, y₁ = 4, x₂ = 0 , y₂ = -3

By section Formula,

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

y = (m₁ × y₂ + m₂ × y₁) / ( m₁ + m₂ )

P(x , y ) = ( 1 × 0 + 4 × (-1) ) / 1+4  , (1 × (-3) + 4 × 4) / 1 + 4

P(x , y) = ( 0 - 4 ) / 5 , ( -3 + 16 ) / 5

P (x , y ) = ( -4 / 5 , 13 / 5 )

Hence, ( -4 / 5 , 13 / 5) is the required Point.