Given the points, l(-2 5) and m(2 -3) point q(6/5 -7/5) partitions line lm in the

If we assume Q lies on the line LM
the ratio LQ:QM can be obtained by
LQ:QM = (Xm-Xl):(Xq-Xm)
=(6/5-(-2)) :  (2-6/5)
=16/5:4/5
=16:4
=4:1

However, we cannot assume that Q lies on LM, so we need to check by using the y-coordinates:
LQ:QM = (Ym-Yl):(Yq-Ym)
=(-7/5-5) : (-3-(-7/5)
=32/5: 8/5
=32:8
=4:1   as before => Q lies on line LM

Therefore LQ:QM = 4:1

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