The point that partitions AB so that AC : CB = 1:3 is (x, y) = (0.25, 3.5). Option D
How do we find the point that partitions AB?
(x, y) = ((m×x₂ + n × x₁)/m+n, (m×y₂ + n × y₁)/m+n)
(x,y₁) are the coordinates of point A.
(x₂, y₂ ) are the coordinates of point B.
m : n is the ratio in which C divides AB.
Given the ratio AC:CB = 1:3, we can calculate the coordinates of C as:
(x, y) = (1×4+3×(−1)/1+3, 1×8 + 3×2/1 + 3)
(x, y) = (1/4, 14/4)
(x, y) = (0.25, 3.5)