Partioning a line segment

Question

What point along line segment AB would split the line into 2:3 Ratio if A(-5,9) and B(8,-2)

Answer 1

The line segment AB goes from point A(-5,9) to point B(8,-2).

Using the distance formula (based on the Pythagorean Theorem), we may find the length of segment AB, then calculate the point C that splits line segment AB into line segments AC and CB.  Then, again using the Pythagorean Theorem, we may calculate the coordinates of point C.

The result will be that the x-coordinate of C will be (2/5)ths of the distance from -5 to 8.  The y-coordinate of C will be (2/5)ths of the distance from 9 to -2.  So, let’s just calculate those and save a lot of intermediate calculations.

(2/5)(8-(-5)) = (2/5)(13) = 26/5 = 5 1/5 = 5.2

(2/5)(-2-(9)) = (2/5)(-11) = -22/5 = -4 2/5 = -4.4

   The coordinates of C (the point along line segment AB that would split the line into 2:3 Ratio) are:

        C(5.2,-4.4)