Geometry question

Question

What are coordinates of the point on the directed líne segment from (- 6, - 6) to \ 9,-1) that partitions the segment into a ratio of 2 to 3?

Answer 1

ratio of 2:3 means 2/5 of the way up the line

-6 to 9 is 15. 2/5 times 15 = 6. 6+(-6) = 0 = x coordinate of the partitioning point

-6 to -1 is 5. 2/5 times 5 = 2. 2+(-6) = -4 = y coordinate of the partitioning point

(0,-4) partitions the line segment into a ratio of 2:3