I would tend to agree, but there is another answer which (IMHO) should also be acceptable, making this an ambiguous question.
Most sources (Wikipedia, for example) list the houses of York and Lancaster (as well as the house of Anjou) as separate from that of Plantagenet, which makes Richard II (Richard the Second) the last Plantagenet.
On its Richard III page however, Wikipedia describes Richard III as "the last king of the House of York and the last of the Plantagenet dynasty".
A nice distinction. Richard III was the last king of the Plantagenet dynasty, but the last king of the House of Plantagenet was Richard II. IMHO, the way this question was phrased leaves enough doubt to make "Richard II" an acceptable answer.
© Haydn Thompson 2017