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The scale drawing shows the positions of two towns, A and B - OCR - GCSE Maths - Question 9 - 2023 - Paper 2
Question 9
The scale drawing shows the positions of two towns, A and B. Scale: 1 cm represents 10 km (a) Find the actual distance between town A and town B. (b) Town C is 55... show full transcript
Worked Solution & Example Answer:The scale drawing shows the positions of two towns, A and B - OCR - GCSE Maths - Question 9 - 2023 - Paper 2
Step 1
Find the actual distance between town A and town B.
Answer
To find the actual distance between towns A and B, we first measure the distance on the scale drawing between town A and town B. Let's say the distance measured is 'x' cm.
Using the scale of 1 cm representing 10 km, we can calculate the actual distance as:
Therefore:
Step 2
Town C is 55 km from town B on a bearing of 330°.
Answer
To mark the position of town C, we begin at town B on the scale drawing. We need to measure 55 km from town B, which corresponds to:
ext{Distance in cm} = rac{55 ext{ km}}{10 ext{ km/cm}} = 5.5 ext{ cm}
Next, we identify the bearing of 330°, which is measured from the North towards the west. We then measure an angle of 330° clockwise from the North and place a mark at a distance of 5.5 cm from town B. Finally, we label this mark as town C.