Question

Draw a line segment AB and by ruler and compasses, obtain a line segment of length $\frac{3}{4}\left(AB\right)$.

Answer 1

Steps of construction:

(i) Draw a line segment AB.

(ii) Draw a ray AX making an acute angle with AB and mark 4 equal parts at $A_1,A_2,A_3,A_4.$

(iii) Join $A_{4}B.$

(iv) From $A_3$, draw a line parallel to $A_{4}B$ which meets AB at C.

C is the required point and AC = $\frac{3}{4}\left(AB\right)$.