Drawing and Bisecting Line Segments

A line segment is a straight path between two fixed points. Learn how to draw segments of a given length, measure them, and find the midpoint using a compass.

Lines, Rays, and Line Segments

Before drawing, it helps to know the difference between three similar ideas:

Name	Description	Ends?
Line	Goes on forever in both directions	No ends
Ray	Starts at a point and goes on in one direction	One end
Line segment	Has two endpoints — a fixed start and finish	Two ends

A line segment is the one you can actually measure and draw. We write it as $\overline{AB}$ , where $A$ and $B$ are the endpoints.

Drawing a Line Segment with a Ruler

1
Mark the start point
Draw a dot and label it $A$ .
2
Place the ruler
Put the 0 cm mark exactly on point $A$ .
3
Mark the length
Find the desired length on the ruler and draw a dot there — label it $B$ .
4
Draw the segment
Draw a straight line from $A$ to $B$ along the ruler edge.

Drawing a 6 cm segment

Place the ruler so 0 cm is at $A$ . Make a mark at 6 cm and label it $B$ . Draw $\overline{AB}$ . The segment is exactly 6 cm long.

Tip Always read the ruler from the 0 mark, not from the edge of the ruler, which may have a small gap.

Measuring Line Segments

To measure $\overline{AB}$ , place the 0 cm mark at $A$ and read the number at $B$ . Write the length as $|AB| = \ldots$ cm.

Real world: measuring furniture

Furniture makers measure every piece of wood using a ruler or tape measure. A shelf 80 cm long is a line segment — it has two ends and a fixed length.

On a scale drawing of a room, 1 cm on the drawing might equal 50 cm in real life. If a sofa measures 3 cm on the plan, it is $3 \times 50 = 150$ cm long in reality.

Bisecting a Line Segment (Finding the Midpoint)

The midpoint $M$ of $\overline{AB}$ is the point exactly halfway between $A$ and $B$ .

Midpoint

M = \frac{|AB|}{2}

The midpoint divides the segment into two equal halves.

With a ruler (quick method): measure the total length, divide by 2, then mark that distance from $A$ .

With a compass and ruler (exact method):

1
Open the compass
Set the compass to more than half the length of $\overline{AB}$ .
2
Draw arcs from A
With the compass tip on $A$ , draw an arc above and below the segment.
3
Draw arcs from B
Without changing the compass width, place the tip on $B$ and draw two more arcs so they cross the first arcs.
4
Connect the intersections
Draw a straight line through the two crossing points. Where this line crosses $\overline{AB}$ is the midpoint $M$ .

Bisecting a 10 cm segment

$\overline{AB} = 10$ cm. Using the compass method, we find $M$ at 5 cm from $A$ . Check: $|AM| = |MB| = 5$ cm. ✓

Parallel and Perpendicular Lines

Two lines are parallel if they never meet and are always the same distance apart. We write $\ell_1 \parallel \ell_2$ .

Two lines are perpendicular if they meet at exactly 90°. We write $\ell_1 \perp \ell_2$ .

Tip The corner symbol (a small square) drawn at the intersection shows that two lines are perpendicular.

Real world: maps and scale drawings

On a street map, roads that run side by side without crossing are parallel. Roads that cross at right angles are perpendicular — think of a typical city grid.

On a construction plan, walls are drawn as parallel line segments. The bisect technique helps builders find the centre of a beam or wall exactly.

Common Mistakes

Reading the ruler from the wrong end (e.g. starting at 1 cm instead of 0 cm)
Not setting the compass wider than half the segment before bisecting
Confusing a line (infinite) with a line segment (has two endpoints)
Pressing too hard with the compass, making holes in the paper

Practice Problems

Draw a line segment of 7.5 cm and label it PQ. What is |PQ|?

Show answer

|PQ| = 7.5 cm. Place the ruler at 0 cm, mark at 7.5 cm, draw the segment.

The midpoint of AB is M and |AM| = 4 cm. What is the total length |AB|?

Show answer

|AB| = 2 × 4 cm = 8 cm.