You can only ask one question per post. I will do question number 1. If segment AB is divided into a ratio of 2:3, that means point M is found 2/5s of the way down the segment AB (starting from point A).
So if the change in the x-direction from point A to point B +20, then point M is found 2/5 of 20 away from point A, which is 8. So x-value of point M is 8.
And if the change in the y-direction from point A to point B is -15, then point M is found 2/5 of -15 away from point A, which is -6. So -6 from 15 is the y-value of 9. So the y-value of point M is 9.
So point M is (8,9). The answer is A.
