Explanation — Perpendicular Bisector of a 6 cm Line
Goal: Draw a line of 6 cm, construct its perpendicular bisector, and show that the line is cut into two equal parts.
What you need
- Ruler (with centimeters)
- Compass
- Pencil
- Eraser (optional)
Step 1 — Draw the line segment
- Use the ruler to draw a straight line segment AB of 6 cm.
- Mark the end points clearly as A and B.
Step 2 — Open the compass
- Place the compass needle at point A.
- Open the compass a little more than half of AB (a bit more than 3 cm). Do not change this setting until Step 3 finishes.
Step 3 — Draw two arcs from A and B
- With the needle at A, draw one arc above the line and one arc below the line.
- Without changing the compass width, place the needle at B.
- Draw another arc above and another below the line so that the arcs cross the earlier arcs.
- Mark the two arc intersection points as P (above) and Q (below).
Step 4 — Draw the perpendicular bisector
- Use the ruler to join P and Q.
- The line PQ is the perpendicular bisector of AB.
- Let M be the point where PQ cuts AB.
Step 5 — Measure the two parts
- Measure AM with the ruler.
- Measure MB with the ruler.
We know the total length is (6 ext{ cm}).
The perpendicular bisector cuts the line into two equal halves.
So each half is ( rac{6 ext{ cm}}{2} ).
( rac{6}{2} = 3 ).
Therefore, ( AM = 3 ext{ cm} ) and ( MB = 3 ext{ cm} ).
Why this works (in simple words)
- Arcs from A and B with the same compass width find points that are the same distance from A and B.
- Joining these points gives a line that is exactly in the middle and also at right angles (90°) to AB. That’s why it is called a perpendicular bisector.
Final Result
Each part = 3 cm. So, ( AM = MB = 3 ext{ cm} ).