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Direction: Study the following information and answer the question given below. There is an MN axis such that M is in the north direction and N is in the south direction. There is a PQ axis such that P is in the west direction and Q is in the east direction. The MN axis and PQ axis intersect at a point O such that MO = 13 km, ON = 15 km, OP = 10 km, and OQ = 22 km. Robert starts walking from point P and walks 18 km south, then turns left and walks 30 km. Nicholas starts walking from point M and walks 20 km east. What is the distance between Nicholas's current position and Robert's current position?
- 31 km
- 33 km
- 11 km
- 20 km
Correct answer: 31 km
Solution
Take O as the origin. Then P is at (-10,0) and M is at (0,13). Robert goes 18 km south from P to (-10,-18), then 30 km left (east) to (20,-18). Nicholas goes 20 km east from M to (20,13). The vertical distance between them is 31 km, and the horizontal distance is 0, so the total distance is 31 km.
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