Question

Draw a line segment $AB=3.5$ cm. Located a point P such that $PA=2.5$ cm and $PB=3$ cm. Produce $PA$ up to point $A^{\prime }$ such that $P{A}^{\prime }=3PA$ and produce $PB$ up to $B^{\prime }$ such that $P{B}^{\prime }=3PB$.
Join $A^{\prime }$ and $B^{\prime }$. Find the ratio $\frac{A^{\prime }{B}^{\prime }}{AB}.$

• A. $2$
• B. $3$
• C. $4$
• D. $5$

Answer 1

The correct option is B $3$

In the figure

$△ABP$ and $△P{B}^{\prime }{A}^{\prime }$ are similar

$\frac{A^{\prime }{B}^{\prime }}{AB}=\frac{P{A}^{\prime }}{PA}=\frac{P{B}^{\prime }}{PB}$

consider, $\frac{A^{\prime }{B}^{\prime }}{AB}=\frac{P{A}^{\prime }}{PA}$

$\frac{A^{\prime }{B}^{\prime }}{AB}=\frac{3PA}{PA}$ ------given, $P{A}^{\prime }=3PA$

$\frac{A^{\prime }{B}^{\prime }}{AB}=3$ Option B