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Draw a line LPQ = 7.5cm and construct a perpendicular at A to B

Mathematics

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Here are the steps to draw a line segment PQ of 7.5 cm and construct its perpendicular bisector. I will assume "construct a perpendicular" refers to constructing a perpendicular bisector of PQ, as the phrase "at A to B" is unclear in the context of line segment PQ.

  1. Draw a line segment PQ that is 7.5 cm7.5 \text{ cm} long using a ruler.

    Mark the endpoints as P and Q.

  2. Place the compass needle at point P.

    Open the compass to a radius greater than half the length of PQ (i.e., greater than 3.75 cm3.75 \text{ cm}). Draw an arc above and an arc below the line segment PQ.

  3. Without changing the compass radius, place the compass needle at point Q.

    Draw an arc above and an arc below the line segment PQ, ensuring these arcs intersect the previously drawn arcs.

  4. Label the two points where the arcs intersect as R and S.

  5. Use a ruler to draw a straight line connecting point R and point S.

    This line RS is the perpendicular bisector of PQ, and it will pass through the midpoint of PQ.

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