Class 10 Division of a Line Segment — practice questions with answers
Geometry · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.
1. To divide a line segment AB internally in the ratio 3 : 2 by the basic construction, how many points must be marked on the ray AX at equal distances?
A2
B3
C5
D6
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Answer: C) 5
The number of equal points needed equals the sum of the ratio terms, 3 + 2 = 5.
2. While dividing AB in ratio 3 : 2, the equal arc spacing on ray AX must be:
AEqual to AB
BAny convenient but equal length
CExactly 1 cm always
DDecreasing in size
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Answer: B) Any convenient but equal length
Arcs of any convenient length are fine, but they must all be equal so the segment is split correctly.
3. If AP : PB = 1 : 1 and AB = 16 cm, then AP = ____ cm.
A16
B9
C7
D8
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Answer: D) 8
1 : 1 means P is the midpoint, so AP = 216 = 8 cm.
4. Segment AB = 45 cm is divided in ratio 4 : 5 at P. The midpoint M of AB also lies on AB. Find the distance PM in cm.
A5
B2.5
C3.5
D1.5
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Answer: B) 2.5
AP = 94x45 = 20, AM = 245 = 22.5. PM = 22.5 - 20 = 2.5 cm.
5. A segment AB = 90 cm is divided into pieces in the continued ratio 1 : 2 : 3 : 4 by three internal points P, Q, R (in order from A). Find the distance AR in cm.
A49
B59
C108
D54
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Answer: D) 54
Total parts = 1+2+3+4 = 10, each part = 9 cm. AR covers the first three pieces = (1+2+3) parts = 6 parts = 54 cm.