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If you want to divide a 10 cm line into two equal parts using a compass, how far should the compass be opened?
- a)2.5 cm
- b)5 cm
- c)10 cm
- d)15 cm
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
If you want to divide a 10 cm line into two equal parts using a compas...
Understanding the Problem
To divide a 10 cm line into two equal parts, we need to find the midpoint of the line. The midpoint of a line segment is exactly halfway between its endpoints.
Finding the Midpoint
The total length of the line is 10 cm. To find the midpoint:
- Calculate:
- Midpoint = Total Length / 2
- Midpoint = 10 cm / 2 = 5 cm
This tells us that each half of the line will be 5 cm long.
Using a Compass to Divide the Line
To divide the line into two equal parts using a compass, you need to perform the following steps:
1. Open the Compass:
- Set the compass to a width of 5 cm. This is crucial because it allows you to draw arcs from both endpoints of the line.
2. Draw Arcs:
- Place the compass point on one endpoint of the line and draw an arc above and below the line.
- Without changing the compass width, repeat this from the other endpoint of the line.
3. Intersecting Points:
- The arcs will intersect at two points above and below the line.
4. Draw the Midpoint Line:
- Use a ruler to draw a straight line connecting the two intersection points. This line will intersect the original line, marking the midpoint.
Conclusion
Thus, to accurately divide a 10 cm line into two equal parts using a compass, it is essential to open the compass to 5 cm. This method ensures precision in finding the midpoint and effectively divides the line into two equal sections.
To divide a 10 cm line into two equal parts, we need to find the midpoint of the line. The midpoint of a line segment is exactly halfway between its endpoints.
Finding the Midpoint
The total length of the line is 10 cm. To find the midpoint:
- Calculate:
- Midpoint = Total Length / 2
- Midpoint = 10 cm / 2 = 5 cm
This tells us that each half of the line will be 5 cm long.
Using a Compass to Divide the Line
To divide the line into two equal parts using a compass, you need to perform the following steps:
1. Open the Compass:
- Set the compass to a width of 5 cm. This is crucial because it allows you to draw arcs from both endpoints of the line.
2. Draw Arcs:
- Place the compass point on one endpoint of the line and draw an arc above and below the line.
- Without changing the compass width, repeat this from the other endpoint of the line.
3. Intersecting Points:
- The arcs will intersect at two points above and below the line.
4. Draw the Midpoint Line:
- Use a ruler to draw a straight line connecting the two intersection points. This line will intersect the original line, marking the midpoint.
Conclusion
Thus, to accurately divide a 10 cm line into two equal parts using a compass, it is essential to open the compass to 5 cm. This method ensures precision in finding the midpoint and effectively divides the line into two equal sections.
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If you want to divide a 10 cm line into two equal parts using a compas...
To divide a 10 cm line into two equal parts, open the compass to 5 cm.
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If you want to divide a 10 cm line into two equal parts using a compass, how far should the compass be opened?a)2.5 cmb)5 cmc)10 cmd)15 cmCorrect answer is option 'B'. Can you explain this answer?
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