Question

Question 75

Draw a line segment of length 7 cm. Draw its perpendicular bisector, using ruler and compass.

Answer 1

A perpendicular bisector is a kind of line segment, ray, or line that: (1) intersects a given segment at a ${90}^{\circ }$ angle, and. (2) passes through the given segment's midpoint.

Steps of construction:

Step I: Draw a line segment, $\overline{PQ}=7cm$

Step II: With P as centre and a convenient radius $morethan\frac{1}{2}\overline{PQ}$, draw an arc above and below the line.

Step III: With Q as centre and same radius, draw another arc, such that it intersects the previous arc at A and B.

Step IV: Join A and B.

Thus, $\overline{AB}$ is perpendicular bisector of $\overline{PQ}$

i.e. OP = OQ = 3.5 cm and $\overline{AB}$ is perpendicular to $\overline{PQ}$.