Photo AI
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 bui... 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
-
Draw the angle bisector: Start by drawing the angle bisector at point A between lines AB and AC. This divides the angle into two equal angles, indicating equal distances to the roads from A to B and A to C.
-
Measure the distance: Since the distance from town C must be less than 14 km, which is equivalent to 7 cm on the scale diagram, draw a circle centered at point C with a radius of 7 cm. This represents all points within 14 km from town C.
-
Shade the region: The area that meets both criteria (nearer to line AB and within 7 cm from C) is where the center of the shopping centre could be. This region will be the overlap of the area closer to AB, below the angle bisector, and within the circle around C.
-
Indicate the correct region: Clearly highlight the shaded region on the diagram for visual clarity.
Step 2
Explain why the region found in part (a) may not be an appropriate site for the shopping centre.
Answer
The region found in part (a) may not be an appropriate site for the shopping centre because:
-
Accessibility: If the road from A to B is busier than the road from A to C, then being closer to road AB does not guarantee easy access for shoppers coming from town C.
-
Urban Planning Requirements: The land use regulations in the zone around town C may not permit commercial construction so close to the town center, especially considering potential traffic and noise generated from the shopping centre.
-
Topography and Land Suitability: The physical characteristics of the land may not be suitable for construction due to factors such as elevation, flood risk, or geological stability.