Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11

# 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). - Mathematics

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).

#### 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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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 23 The straight lines
Exercise 23.12 | Q 9 | Page 93