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Question
Find the equation of a line which is perpendicular to the line joining (4, 2) and (3, 5) and cuts off an intercept of length 3 on y-axis.
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Solution
Let m be the slope of the required line.
Here, c = y-intercept = 3
Slope of the line joining the points (4, 2) and (3, 5) = \[\frac{5 - 2}{3 - 4} = - 3\]
It is given that the required line is perpendicular to the line joining the points (4, 2) and (3, 5).
\[\therefore m \times \text { Slope of the line joining the points }\left( 4, 2 \right) \text { and } \left( 3, 5 \right) = - 1\]
\[ \Rightarrow m \times \left( - 3 \right) = - 1\]
\[ \Rightarrow m = \frac{1}{3}\]
Substituting the values of m and c in y = mx + c, we get,
\[y = \frac{1}{3}x + 3 \]
\[ \Rightarrow x - 3y + 9 = 0\]
Hence, the equation of the required line is x \[-\] 3y + 9 = 0
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