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Standard XII

Mathematics

Condition for Two Lines to Be Parallel

A line AB m...

Question

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

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Solution

Slope of $A B (m) = \frac{y_{2} y_{1}}{x_{2} - x_{2}} = \frac{- 3, - 0}{0 - 6}$
$= \frac{- 3}{- 6} = \frac{1}{2}$
Slope of perpendicular bisector of $A B$
$m_{2} = - \frac{1}{m} = - \frac{1}{- 1 / 2} = - 2$
Equation of required line
$y - y_{1} = m (x - x_{1})$
$y - (- 1) = - 2 (x - 4)$
$\Rightarrow y + 1 = - 2 x + 8$
$\Rightarrow 2 x + y = 7$

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A line AB meets X-axis at A and Y-axis at B.P(4,−1) divides AB in the ratio 1:2. Find the equation of the line through P and perpendicular to AB

Slope of AB(m)=y2y1x2−x2=−3,−00−6=−3−6=12Slope of perpendicular bisector of ABm2=−1m=−1−1/2=−2Equation of required liney−y1=m(x−x1)y−(−1)=−2(x−4)⇒y+1=−2x+8⇒2x+y=7

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