ICSE Class X Math 2016 Solved Paper

A line $A B$ meets $X$ -axis at $A$ and $Y$ -axis at $B$ . $P(4,-1)$ divides $A B$ in the ratio $1: 2$ .

Question : 37 of 57

Marks: +1, -0

Find the equation of the line through

P

and perpendicular to

A B

Solution:

Slope of

{\AB}(m)\;=\;{y_2-y_1}/{x_2-x_1}

\;=\;{-3-0}/{0-6}=\;{-3}/{-6}=\;{1}/{2}

Slop of perpendicular bisector of

A B

m_2=-\;{1}/{m}=-\;{1}/{1 \/ 2}=-2

Equation of required line

y-y_1\;=m (x-x_1)

\;y-(-1)\;=-2(x-4)

⇒ y+1\;=-2 x+8

⇒ 2 x+y=7\;

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