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Anita starts from her house at Point A and walks 5 m towards South. She takes a right turn, walks 7 m, takes another right and walks 12 m and stops at point P. If a pole is placed 7 m towards East from where she stopped (Point P), how far (shortest distance) and in which direction will her house be from the pole? (All turns are 90 degrees turns only unless specified.)
12 m towards South
7 m towards East
7 m towards South
5 m towards North
12 m towards South
Track Cartesian coordinates step-by-step from Point A (0,0) and use final offset coordinates to determine exact distance and direction.
Track Cartesian coordinates step-by-step from Point A (0,0) and use final offset coordinates to determine exact distance and direction.
Step 1: Movement from House (Point A)
Anita starts from her house at Point A (0, 0) and walks 5 m towards the South, reaching (0, -5).
Step 2: Right Turn and Second Movement
She takes a right turn (facing West) and walks 7 m, reaching coordinates (-7, -5).
Step 3: Second Right Turn and Point P
She takes another right turn (facing North) and walks 12 m, stopping at Point P. Her coordinates become (-7, -5 + 12) = (-7, 7).
Step 4: Pole Position and Final Calculation
A pole is placed 7 m towards East from Point P, placing the pole at (-7 + 7, 7) = (0, 7). Since her house is at (0, 0) and the pole is at (0, 7), her house is exactly 7 m towards the North from the pole.
A: 7 m towards the South is incorrect because the house is at y = 0 and the pole is at y = 7, making the house North of the pole. B: 12 m towards the North miscalculates the vertical distance component. D: 5 m towards the North uses the initial starting step instead of the net calculated difference.
C is correct because Anita's house is at coordinates (0, 0) and the final pole is placed at (0, 7), making the house 7 m towards the North from the pole.
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