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The diagram shows the line segment [AB] - Junior Cycle Mathematics - Question 2 - 2017
Question 2
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The diagram shows the line segment [AB]. Divide the line segment into three equal parts, without measuring it. Show all of your construction lines clearly.
Worked Solution & Example Answer:The diagram shows the line segment [AB] - Junior Cycle Mathematics - Question 2 - 2017
Step 1
Divide the line segment into three equal parts
Answer
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Start with the line segment [AB].
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Construct a ray from point A at an angle, and mark a point X on this ray such that AX measures a convenient length.
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From point X, construct an arc that extends beyond point B, indicating that length AX will be used again.
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Without changing the length, move to points Y and Z by marking out two more segments of length AX from point X on the arc until you reach point B, naming them accordingly.
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Denote the three equal parts of the segment [AB] as segments AX, XY, and YB, ensuring points X, Y, and Z are clearly indicated along the line segment.