a line segment begins at the point (-4, -9) and ends at the point (21, 31.625). What’s the point that splits this line segment into two segments whose lengths are inthe ratio of 2:3

Question

The answer is (6, 7.25). However I want to know how to solve it.

Answer 1

We need to divide the difference in the coordinates by 5, then work out 2/5 and 3/5 of these values so that we can determine the correct split to give us the ratio 2/5 to 3/5 which is 2:3.

Diff between x coords: 21-(-4)=25, so ⅖ of this is 10.

Diff between y coords: 31.625-(-9)=40.625, so ⅖ of this is 16.25.

We want the point ⅖ away from the starting coords so we add these numbers to (-4,-9):

x: -4+10=6 and y: -9+16.25=7.25.

So the point is (6,7.25).

We could have worked out ⅗ instead of ⅖ and subtracted from the end point coords to give the same result:

x: 21-15=6 and y: 31.625-24.375=7.25.