Find the point X which divides the segment between A(2, 3) and B(5, 8) into a ratio of 1 : 3.

Answer 1

Since 1+3 = 4, we are dividing AB into 4 equal segments with point X being 1/4 of the way from A to B.

As we move along AB from A to B, the x-coordinates increase by 3 and the y-coordinates increase by 5.

x-coordinate of X = x-coordinate of A + (1/4)(change in x from A to B) = 2 + (1/4)(3) = 2.75

y-coordinate of X = y-coordinate of B + (1/4)(change in y from A to B) = 3 + (1/4)(5) = 4.25

X = (2.75, 4.25)