Given: Points A,B,C are co-linear on line segment AC , and
AB : BC = m : n= 3 : 4.
Coordinates of A = (x,y) ,
Coordinates of B = (x₁, y₁) = (4,1) , and
Coordinates of C = (x₂, y₂ ) = (12,5).
To find: the values of x and y
Now, we shall apply intersection (internally) formula for point B,
x₁ = (mx₂ + nx ) ÷ (m + n)
4 = (3×12 + 4× x ) ÷ (3 +4)
or, x = - 2 and,
y₁ = (my₂ + ny ) ÷ (m + n)
1 = (3×5 + 4× y ) ÷ (3 +4)
or, y = - 2
Hence, the required point A (x, y) will be (-2, -2)
