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3 Four points A, B, C and D are shown on the scale diagram below - OCR - GCSE Maths - Question 3 - 2017 - Paper 1
Question 3
3 Four points A, B, C and D are shown on the scale diagram below. B C D A Scale: 1 cm represents 5 m a) On the diagram, construct and mark the two points that ... show full transcript
Worked Solution & Example Answer:3 Four points A, B, C and D are shown on the scale diagram below - OCR - GCSE Maths - Question 3 - 2017 - Paper 1
Step 1
Construct and mark the two points that are the same distance from A and B
Answer
To find a point equidistant from points A and B, first, locate the midpoint between A and B. Then, using a compass, draw arcs from points A and B that intersect. The intersection points are the locations equidistant from A and B. Mark these points as P1 and P2.
Step 2
Construct and mark the two points that are 15m from C
Answer
Using a compass set to a distance of 3 cm (since 1 cm represents 5 m), draw an arc from point C. The points where this arc intersects the area of the garden represent the locations that are 15 m away from point C. Mark these intersection points as P3 and P4.
Step 3
Explain why there is only one position where Monty can plant his tree
Answer
There is only one position where Monty can plant his tree because the points P1 and P2, which are equidistant from A and B, must also satisfy the condition of being 15m from point C. The intersection of the arcs created at P1 and P2 with the arc from point C will yield a unique point where all conditions intersect, meaning there is only one viable planting position.