points L,M,N are collinear such that LM:LN = 4/9. Point L is located at (-3,-7). Point M is located at (j,k), and point N is located at (-3,11). what are the values of j and k.

Answer 1

First, notice that points L and N have the same x-coordinate, -3. Therefore this line is a vertical line and the x-coordinate of point M is also -3, so we have M = (-3, k).

Line LN has a length of y_N - y_L = 11 - (-7) = 18. Point M is 4/9 of 18 higher up the line than point L. So the y-coordinate of point M is k = -7 + (4/9)(18) = -7 + 8 = 1.

M = (-3, 1)