ICSE Class X Math 2015 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

\therefore

Coordinates of

P

\left( \frac{m_1 x_2 + m_2 x_1}{m_1+m_2}, \; \frac{m_1 y_2 + m_2 y_1}{m_1+m_2} \right)

= \left( \frac{-2k+y}{k+1}, \; \frac{-4k}{k+1} \right)

Let coordinates of

P

(x, y)

x = \frac{-2k+4}{k+1}

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

2k = 4 \Rightarrow k=2

\text{Ratio} = 2:1

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