Help with this one optic question from kaplan?

[m25]

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I've attached the scan of the question and its answer explanation.

Can you help me figure out why they are using o=50 and i=-100cm?

How do you know to put a negative sign for i??

 

[Cawolf]

The object distance is 50 cm because that is where your friend, the object, is standing.

The image distance is the distance you can focus on, the near point. The distance is negative because it is on the same side of the lens as the real object (the friend). This is convention to align with the thin lens formula.