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The scale diagram below shows towns, A, B and C - OCR - GCSE Maths - Question 7 - 2018 - Paper 1
Question 7
The scale diagram below shows towns, A, B and C. Line AB represents the road from A to B and line AC represents the road from A to C. A shopping centre is to be ... show full transcript
Worked Solution & Example Answer:The scale diagram below shows towns, A, B and C - OCR - GCSE Maths - Question 7 - 2018 - Paper 1
Step 1
Using construction, shade the region where the shopping centre could be built.
Answer
To find the region where the shopping centre can be built, follow these construction steps:
- Constructing the angle bisector:
- Use a compass to draw an arc from point A that intersects both lines AB and AC. This can be done by selecting a suitable radius for the arc.
- Label the points where the arc intersects line AB as D and line AC as E.
- With the same radius, place the compass on points D and E and draw two arcs above and below the segment DE. The intersection points of these arcs will determine the angle bisector.
- Shading the region closer to line AB:
- Since the shopping centre must be nearer to road AB than road AC, draw a line parallel to line AC through point A. This line will indicate the area closer to line AB. Shade this area on one side of the angle bisector.
- Establishing the distance from town C:
- Since the shopping centre must be less than 14 km from town C, convert this distance to centimeters on the scale (7 cm on the diagram, as 1 cm represents 2 km).
- Center a compass at point C and draw an arc with a radius of 7 cm. This arc will represent the maximum distance of the shopping centre from town C.
- Shade the area inside this arc.
- Final shaded region:
- The final shaded area that meets both criteria (nearer to road AB and less than 14 km from town C) will be the overlap of the shaded regions from steps 2 and 3.
Step 2
Explain why the region found in part (a) may not be an appropriate site for the shopping centre.
Answer
The region shaded in part (a) may not be an appropriate site for the shopping centre for the following reasons:
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Road Accessibility:
If the closest road is AB but it is significantly busier than road AC, this could deter potential customers from accessing the shopping centre safely. If access is not straightforward, this might affect overall foot traffic and business viability. -
Environmental Considerations:
Depending on the geographic features surrounding town C, there might be environmental restrictions on construction. Areas could be prone to flooding or other natural hazards which may not be suitable for commercial properties. -
Proximity to Other Amenities:
If the shaded region is far from other commercial areas or residential developments, it might not attract enough customers, thus affecting profitability. The effectiveness of a shopping centre often relies on its proximity to other businesses and residential areas. -
Local Regulations:
Local zoning laws or council regulations may prohibit construction in the shaded area based on land-use plans or community development schemes, making it non-viable for development.