Answer in Brief

Find the equation of the straight line perpendicular to 5x − 2y = 8 and which passes through the mid-point of the line segment joining (2, 3) and (4, 5).

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#### Solution

The line perpendicular to 5x − 2y = 8 is \[2x + 5y + \lambda = 0\]

\[\text { Coordinates of the mid points of } \left( 2, 3 \right) \text { and } \left( 4, 5 \right) = \left( \frac{2 + 4}{2}, \frac{3 + 5}{2} \right)\]= (3,4)

\[\therefore 6 + 20 + \lambda = 0\]

\[ \Rightarrow \lambda = - 26\]

Substituting the value of

\[\lambda\] we get

\[2x + 5y - 26 = 0\] , which is equation of the required line.

Concept: Straight Lines - Equation of Family of Lines Passing Through the Point of Intersection of Two Lines

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