Point O is a centroid of the triangle LMN. If OM=38 cm, what is MP? a.) 114 cm
b.) 19 cm
c.) 57 cm
d.) 25.5 cm

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  c.)  57 cm

Step-by-step explanation:

The centroid divides the median into parts with a 2:1 ratio.

  OM : OP = 2 : 1

  OM : MP = 2 : (2+1) = 2 : 3

As a fraction with MP on top, this is ...

  MP/OM = 3/2

  MP = (3/2)OM = 3/2×(38 cm)

  MP = 57 cm

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Comment on the answer choices

Often, you can eliminate a number of the choices in a multiple-choice question just by testing whether they are reasonable. Here, the longer part of a line segment has length 38, so the whole segment will not be shorter than that. The choices 19 and 25.5 make no sense.

The remaining choices are 114 cm and 57 cm. The former is 3 times the length of the given segment, which the drawing tells us is unreasonable.

The only reasonable choice offered is 57 cm.

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step-by-step explanation: