The diagram shows the scale drawing of a garden ABCD - OCR - GCSE Maths - Question 17 - 2019 - Paper 1
Question 17
The diagram shows the scale drawing of a garden ABCD.
Scale: 1 cm represents 5 m
A tree is to be planted in the garden so that it is
• at least 10m from AB
and
• c... show full transcript
Worked Solution & Example Answer:The diagram shows the scale drawing of a garden ABCD - OCR - GCSE Maths - Question 17 - 2019 - Paper 1
Step 1
at least 10m from AB
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Answer
To find the region that is at least 10m from line segment AB, measure 2cm (since 1 cm represents 5m) above the line AB. Draw a parallel line to AB at this distance. This will outline one boundary of the planting region.
Step 2
closer to CD than CB
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Answer
To satisfy the requirement of being closer to CD than CB, first locate the midpoints of segments CD and CB. Construct the perpendicular bisector of segment CB; this line will indicate the boundary where points are equally close to CB and CD. The area on the side closer to CD will be the correct region.
Step 3
at least 15m from D
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Answer
For the condition of being at least 15m from point D, measure 3cm from point D outward in all directions to create a circular boundary. This circle will define another region where the tree cannot be planted.
Step 4
Constructing the shaded region
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Answer
Finally, shade the area that satisfies all the conditions set. This will be the intersection of the regions defined in the previous steps, ensuring that the tree is planted in an area that meets all the required distances from the boundaries.
