Question

Line segment ab has endpoints a(9, 3) and b(2, 6). find the coordinates of the point that divides the line segment directed from a to b in the ratio of 1:2.
a.(4, 6)
b.(6, 4)
c.( 8 3 , 6)
d.( 20 3 , 4)

Answer 1

When we are to divide the line segment such that the ratio is 1:2, there are actually 3 parts of the segment. First, we determine the distance between the coordinates and divide the distance by 3. Then, we add the quotient to the x-coordinate.

x-coordinate:    (2 - 9) / 3 = -7/3
y-coordinate:    (6 - 3 ) / 3 = 1

Adding them to the coordinates of a,
           x - coordinate: (9 - 7/3) = 20/3
           y - coordinate: (3 + 1) = 4
Thus, the coordinates are (20/3, 4).