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The scale drawing represents a park, ABCD - OCR - GCSE Maths - Question 7 - 2021 - Paper 1
Question 7
The scale drawing represents a park, ABCD. Scale: 1 cm represents 10 m. A straight path goes across the park from B. The path is always the same distance from side ... show full transcript
Worked Solution & Example Answer:The scale drawing represents a park, ABCD - OCR - GCSE Maths - Question 7 - 2021 - Paper 1
Step 1
Construct the route followed by the path.
Answer
To construct the path from point B that is equidistant from sides AB and BC, follow these steps:
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Begin by drawing a line perpendicular to side AB from point B. This line represents the shortest distance from B to the line AB.
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Next, draw another line perpendicular to side BC from point B. Ensure that this line is parallel to the previous line.
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The intersection of these lines will create two lines that represent the path across the park. Label this path clearly to indicate the route taken.
Step 2
Construct the locus of the possible positions of the bench.
Answer
To construct the locus for the possible positions of the bench:
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Mark point C on the diagram. Since the bench cannot be more than 50 m away from C, measure 50 m using the scale provided (which is 5 cm on the drawing, as 1 cm = 10 m).
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Using a compass, draw a circle with a radius of 50 m around point C. This circle represents all positions within 50 m of C.
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The indicated area on the path where the bench can be placed will be the intersection of the path and the circle around C. Clearly label this part of the diagram.