test help review pls

Question

 in the coordinate plane has endpoints with coordinates (-4,11) and (8, -1). Find all possible locations for point M so M divides  into two parts with lengths in a ratio of 1:3.

Group of answer choices

(-1,8)

(2,5)

(5,2)

(8,-1)

(-4,11)

Answer 1

(-4,11), (8,-1) has a midpoint which is the average of the coordinates (2,5)

-4 + 8 = 4. 4/2 = 2 = x coordinate of the midpoint

11-1 = 10. 10/2 = 5 = y coordinate of the midpoint

The midpoint divides the line segment in a ratio of 1:1

to get 1:3, find the midpoint between the midpoint and the end point

take the averages again: -4 +2 = -2 -2/2 = -1 = x coordinate

11+5 = 16. 16/2 = 8 = y coordinate

(-1, 8) divides the line segment (-4,11) to (8,-1) in a ratio of 1:3

(5,2) divides the line segment into a ratio of 3:1