ICSE Class X Math 2015 Solved Paper

In the given figure $A B C$ is a triangle and $B C$ is parallel to the $y$ -axis. $A B$ and $A C$ intersects the $y$ -axis at $P$ and $Q$ respectively.

Question : 26 of 52

Marks: +1, -0

Find the ratio in which

Q

divides

A C

Solution:

Let the ratio be

k: 1

∴

Coordinates of

{\P}

(\;{m_1 x_2+m_2 x_1}/{m_1+m_2}, \;{m_1 y_2+m_2 y_1}/{m_1+m_2})

= (\;{-2 k+y}/{k+1}, \;{-4 k}/{k+1})

Let coordinates of

{\P}

(x, y)

x\;=\;{-2 k+4}/{k+1}

0\;=\;{-2 k+4}/{k+1} \;\; \;\text " [as P lies on "\; y \;\text "-axis] "\;

2 k\;=4 ⇒ k=2

\;\text " Ratio "\;\;=2: 1

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