RD Chapter 11 Constructions Ex 11.1 Solutions
Question - 1 : - Determine a point which divides a line segment of length 12 cm internally in the ratio 2 : 3. Also justify your construction.
Answer - 1 : -
Steps of construction :
(i) Draw a line segment AB = 12 cm.
(ii) Draw a ray AX at A making an acute angle with AB.
(iii) From B, draw another ray BY parallel to AX.
(iv) Cut off 2 equal parts from AX and 3 equal parts from BY.
(v) Join 2 and 3 which intersects AB at P.
P is the required point which divides AB in the ratio of 2 : 3 internally.
Question - 2 : - Divide a line segment of length 9 cm internally in the ratio 4 : 3. Also, give justification of the construction.
Answer - 2 : -
Steps of construction :
(i) Draw a line segment AB = 9 cm.
(ii) Draw a ray AX making an acute angle with AB.
(iii) From B, draw another ray BY parallel to AX.
(iv) Cut off 4 equal parts from AX and 3 parts from BY.
(v) Join 4 and 3 which intersects AB at P.
P is the required point which divides AB in the ratio of 4 : 3 internally.
Question - 3 : - Divide a line segment of length 14 cm internally in the ratio 2 : 5. Also justify your construction.
Answer - 3 : -
Steps of construction :
(i) Draw a line segment AB = 14 cm.
(ii) Draw a ray AX making an acute angle with AB.
(iii) From B, draw another ray BY parallel to AX.
(iv) From AX, cut off 2 equal parts and from B, cut off 5 equal parts.
(v) Join 2 and 5 which intersects AB at P.
P is the required point which divides AB in the ratio of 2 : 5 internally.
Question - 4 : - Draw a line segment of length 8 cm and divide it internally in the ratio 4 : 5.
Answer - 4 : -
Steps of construction :
(i) Draw a line segment AB = 8 cm.
(ii) Draw a ray AX making an acute angle with ∠BAX = 60° withAB.
(iii) Draw a ray BY parallel to AX by making an acute angle ∠ABY = ∠BAX.
(iv) Mark four points A1, A2, A3, A4 on AX and five points B1, B2, B3, B4, Bs on BY in such a way that AA1 = A1A2 = A2A3 = A3A4 .
(v) Join A4B5.
(vi) Let this line intersect AB at a point P.
Thus, P is the point dividing the line segment AB internally in the ratio of 4 : 5.