Question

Why do we draw $Q^{\prime }{P}_m\parallel Q{P}_{m+n}$, while constructing the section of the line PQ in the ratio $m:n$?

• A. To make the figure look smaller.
• B. To divide the line PQ in the ratio m:m+n.
• C. To divide the line PQ in the ratio m:n.
• D. To divide the line PQ in the ratio n:m

Answer 1

The correct option is C

To divide the line PQ in the ratio m:n.

By basic proportionality theorem, we know that a line parallel to one side of a triangle divides the other two sides into parts of equal proportion. By construction we know that, $P_m$ divides the line PPm+n in the ratio m:n. when a line $Q^{\prime }{P}_m\parallel Q{P}_{m+n}$ is drawn, it will divide the sides $P{P}_{m+n}$ and $PQ$ in proportion.
Therefore, $\frac{P{Q}^{\prime }}{Q^{\prime }Q}$ = $\frac{P{P}_m}{P_{m}Pm+n}$ = $\frac{m}{n}$. i.e. it will divide the line in the ratio m:n.