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22 The diagram represents a coastline - OCR - GCSE Maths - Question 22 - 2023 - Paper 3

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22 The diagram represents a coastline. A, B and C are lighthouses. A boat is • the same distance from A and B • the same distance from AB and BC. Using a ruler an... show full transcript

Worked Solution & Example Answer:22 The diagram represents a coastline - OCR - GCSE Maths - Question 22 - 2023 - Paper 3

Step 1

Construct the perpendicular bisector of AB

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Answer

  1. Place the compass point on A and draw an arc above and below the line segment AB.
  2. Without changing the compass width, place the point on B and draw another arc that intersects the previous arcs.
  3. Use a ruler to draw a line through the intersection points of the arcs. This line is the perpendicular bisector of AB.

Step 2

Construct the perpendicular bisector of BC

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Answer

  1. Repeat the same process using points B and C. Place the compass point on B and draw arcs above and below line segment BC.
  2. Using the same compass width, place the compass on point C and draw arcs that intersect the previous arcs.
  3. Draw a line through the intersection points, which is the perpendicular bisector of BC.

Step 3

Identify the position of the boat

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Answer

  1. The position of the boat will be at the intersection point of the two perpendicular bisectors (AB and BC).
  2. Label this intersection point as 'Boat'.

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