Question

Points A,B,C are colinear on line segment AC , and AB:BC=3/4. A is located at (x,y) , B is located at (4,1) , and C is located at( 12,5). What are the values of x and y?

Answer 1

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)