The scale 1 cm represents 25 m can be written in the form 1 : k. Find the value of k. The scale drawing represents a harbour. Scale: 1 cm represents 25 m. A boat leaves the harbour from point C and sails on a path that is equidistant from BC and CD. The harbour rules do not allow boats to sail within 75m of point E. Find by construction whether the path of the boat will follow the harbour rules. Show all your construction lines.

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The scale 1 cm represents 25 m can be written in the form 1 : k - OCR - GCSE Maths - Question 9 - 2019 - Paper 1

Question 9

The scale 1 cm represents 25 m can be written in the form 1 : k. Find the value of k. The scale drawing represents a harbour. Scale: 1 cm represents 25 m. A boat ... show full transcript

Worked Solution & Example Answer:The scale 1 cm represents 25 m can be written in the form 1 : k - OCR - GCSE Maths - Question 9 - 2019 - Paper 1

Step 1

Find the value of k.

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Answer

To convert the scale into the form 1 : k, we need to find out how many meters are represented by 1 cm.

Given: 1 cm represents 25 m.

This can be written as:

$1 ext{ cm} : 25 ext{ m}$

To express it in the form 1 : k, we set:

$k = 25$

Thus, the value of k is 25.

Step 2

Find by construction whether the path of the boat will follow the harbour rules.

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Answer

Start by locating points C and E on your scale drawing.
Measure 75m from point E towards the line segment BC and CD, which indicates the prohibited area for the boats.
Draw a line 75m away from point E, parallel to the lines BC and CD. This will clearly show the restricted area.
Now, draw the path from point C, ensuring it remains equidistant from lines BC and CD.
Verify that the drawn path does not intersect with the restricted area.

Follow proper geometric construction techniques to ensure accuracy.

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