Question

The steps involved in dividing a line segment are given below. Arrange them in the correct order.

I. Draw a ray $PM$ making an acute angle with $PQ$

II. Locate m+n points $P_1$, $P_2$, $P_3$......... $P_{m+n}$, such that $P{P}_1$ = $P_1{P}_2$ = $P_2{P}_3$ … = $P_{m+n-1}{P}_{m+n}$.

III. Measure the $\angle$ $P{P}_{m+n}Q$.

IV. Draw a line parallel to $Q{P}_{m+n}$ at $P_m$.

V. Join $Q{P}_{m+n}$.

VI. Draw an angle equal to $\angle$ $P{P}_{m+n}Q$ at $P_m$.

The point Q' at which the line $P_{m}Q\text{'}$ intersects PQ divides the line PQ in the ratio $m:n$

• A. I, III, IV, V, II, VI
• B. I, IV, III, V, II, VI
• C. I, II, V, III, VI, IV
• D. I, II, III, V, IV, VI

Answer 1

The correct option is C

I, II, V, III, VI, IV

The procedure in dividing a line segment with the help of a single ray is:

I. Draw a ray $PM$ making acute angle with $PQ$.

II. Locate $m+n$ points $P_1$, $P_2$, $P_3$......... $P_{m+n}$, such that $P{P}_1$ = $P_1{P}_2$ = $P_2{P}_3$ … = $P_{m+n-1}{P}_{m+n}$.

III. Join $Q{P}_{m+n}$.

IV. Measure the $\angle$ $P{P}_{m+n}Q$.

V. Draw an angle equal to $\angle$ $P{P}_{m+n}Q$ at $P_m$.

VI. Draw a line parallel to $Q{P}_{m+n}$ at $P_m$.

The point Q' at which the line $P_{m}Q\text{'}$ intersects PQ divides the line PQ in the ratio $m:n$

Therefore the correct order would be, I, II, V, III, VI, IV.