How to Bisect a Line with Ruler and Compass

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How to Bisect a Line with Ruler and Compass
How to Bisect a Line with Ruler and Compass
Anonim

In drawings with ruler and compass it may happen to use a ruler on which the measurement notches are missing (unlike a ruler with graduated scale). So how do you bisect (find the center of) a line and draw an axis perpendicular to the segment if it cannot be measured? The answer is to use the compass. Here's how to proceed.

Steps

Bisect a Line With a Compass and Straightedge Step 1
Bisect a Line With a Compass and Straightedge Step 1

Step 1. Start by drawing a straight line of any length so that it can be covered by the compass opening

Draw it with the ruler.

Bisect a Line With a Compass and Straightedge Step 2
Bisect a Line With a Compass and Straightedge Step 2

Step 2. Place the compass needle on one end of the segment. Open the compass so as to cover more than half the distance to the other end.

Bisect a Line With a Compass and Straightedge Step 3
Bisect a Line With a Compass and Straightedge Step 3

Step 3. Draw two arcs, one above and one below the line

Bisect a Line With a Compass and Straightedge Step 4
Bisect a Line With a Compass and Straightedge Step 4

Step 4. Without changing the opening length of the compass, place the needle of the tool on the other end of the line

Bisect a Line With a Compass and Straightedge Step 5
Bisect a Line With a Compass and Straightedge Step 5

Step 5. Draw two more arcs, one above and one below the segment

These arcs have the same radius as the first two.

Bisect a Line With a Compass and Straightedge Step 6
Bisect a Line With a Compass and Straightedge Step 6

Step 6. Align the ruler to connect the intersections of the arcs and draw a line from one point to another of the intersections

This line will cut the line into two equal parts.

Advice

  • Make sure the lead on the compass is pointed. If the lead is worn, the width of the drawn lines will cause measurement errors when positioning the ruler or compass needle.
  • Why it works. You are basically turning the drawn segment into the diagonal of a rhombus. In fact, the rotation of the compass marks the ends of the four sides of the rhombus - you just don't need to draw them by connecting the points. So when you connect the two Xs formed by the arcs, you are actually drawing the other diagonal of the rhombus. In fact, one of the characteristic properties of a rhombus is that the longest and the shortest diagonals are perpendicular to each other, where the longer diagonal intersects the shorter one. So, the line connecting the two Xs represents the bisector of the line you initially drew.
  • If the two arcs do not intersect, it means that either the drawn arcs are not long enough, or you have not opened the compass sufficiently. Erase the arcs, open the compass more, and try again.

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