Question

line segment jk in the xy-coordinate plane has endpoints with coordinates (-4,11) and (8,-1). what are two possible locations for point M so that M divides JK into two parts with lengths in a ratio of 1:3?

Answer 1

-12/12 I think would be M.

Answer 2

M divides JK into two parts with lengths in a ratio of 1:3

so JM:MK is either 3:1 or 1:3

before solving for M, need to find mid-pt of JK, point L

L is at (-4+8)/2 and (11-1)/2 so L is at (2,5)

mid-pt of JL is at (-4+2)/2 and (11+5)/2 so it is at (-1,8)
and mid-pt of LK is at (8+2)/2 and (-1+5)/2 so it is at (5,2)

note that these pts are the fourths. They divide the segment into fourths, so the three-quarter segment is indeed thrice as long as the quarter segment. They are the ans for pt M.

M is (-1,8) or (5,2)