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ICSE Class X Math 2016 Paper

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A line ABA B meets XX-axis at AA and YY-axis at BB.P(4,−1)P(4,-1) divides ABA B in the ratio 1:21: 2.
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Question : 37 of 57
Marks: +1, -0
Find the equation of the line through PP and perpendicular to ABA B.
Solution:  
Slope of AB(m)  =y2−y1x2−x1AB(m)\;=\frac{y_2-y_1}{x_2-x_1}
  =−3−00−6=−3−6=12\;=\frac{-3-0}{0-6}=\frac{-3}{-6}=\frac{1}{2}
Slop of perpendicular bisector of ABA B
m2=−  1m=−  112=−2m_2=-\;\frac{1}{m}=-\;\frac{1}{\frac{1}{2}}=-2
Equation of required line
y−y1  =m(x−x1)y-y_1\;=m (x-x_1)
  y−(−1)  =−2(x−4)\;y-(-1)\;=-2(x-4)
⇒y+1  =−2x+8\Rightarrow y+1\;=-2x+8
⇒2x+y=7  \Rightarrow 2x+y=7\;
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