Tran is using a coordinate plane to design a treasure hunt for his students. The hunt begins at the flagpole at the origin. The
1 answer:
Answer:
The shortest combined distance along the path from the flagpole to Clue 1 to Clue 2 and to Clue 3 is approximately 1,031.025 feet
Step-by-step explanation:
The given coordinates of the clues for the treasure hunt are
The location of the first clue = 5 units north of the flag pole
The coordinates is (0, 5)
The location of the second clue = 6 units east of the flag pole
The coordinates is (6, 0)
The location of the final clue = 5 units south of the flag pole
The coordinates is (0, -5)
The flagpole is at the origin
The coordinates of the flagpole is (0, 0)
Each unit on the graph = 50 feet
From the drawing of the treasure hunt created with Microsoft Excel, the shortest distances between the clues are as follows;
The shortest distance between 2 points is a straight line
Therefore
The shortest length from the flagpole to Clue 1 = 5 - 0 = 5 units
The actual distance from the flagpole to Clue 1 = 5 units × 50 feet/unit = 250 feet
The length from Clue 1 to Clue 2= √(6² + 5²) = √(61) units
The actual distance from Clue 1 to Clue 2 = √(61) units × 50 feet/unit = 50·√61 feet
By similarity, the actual distance from Clue 2 to Clue 3 = 50·√61
The combined shortest distance along the path from the flagpole to Clue 1 to Clue 2 and to Clue 3 = (250 + 50·√61 + 50·√61) feet ≈ 1,031.025 feet
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