Divide a line segment 11 cm in the ratio of 2 : 5 (a) internally (b) externally.
(i) Draw AB =11 cm.
(ii) Draw a ray AX making an acute ∠ BAX.
(iii) Along AX, mark points A1, A2, A3 .........,
A7. Such that AAl = A1A2 = .......= A6A7.
(iv) Join A7 B.
(v) Through A2, draw a line A2C || A7B intersecting AB at C.
Thus, point C so obtained is the required point which divides AB internally in the ratio 2
: 5.
(b) Externally : Steps of Construction
(i) Draw AB = 11 cm.
(ii) Draw a ray BX making an acute ∠ ABX.
(iii) Along a ray BX, mark points B1, B2,..., B5, such that BB1 = B1B2 = B2B3 =
B3B4= B4B5.
(iv) Join B3A.
(v) Through B5, draw a line parallel to B3A intersecting BA produced at C.
Thus, point C so obtained is the required point which divides AB externally in the ratio 2 : 5.
Constructions Based on similar triangle
