First slide

Equation of line in Straight lines

Question

Let the equation of two sides of a triangle be $3 x - 2 y + 6 = 0$ and $4 x + 5 y - 20 = 0$ . If the orthocentre of this triangle is at (1,1). then the equation of its third side is

Moderate

A

$26 x - 122 y - 1675 = 0$
B

$26 x + 61 y - 1675 = 0$
C

$122 y - 26 x - 1675 = 0$
D

$122 y - 26 x + 1675 = 0$

Solution

$4 x + 5 y - 20 = 0$ ………(1)
$3 x - 2 y + 6 = 0$ …….. (2)
orthocentre is (1,1)
lien perpendicular to $4 x + 5 y - 20 = 0$ and passes through (1,1) is $(y - 1) = \frac{5}{4} (x - 1)$
$\Rightarrow 5 x - 4 y = 1....... (3)$
and line perpendicular to $3 x - 2 y + 6 = 0$ and passes through (1,1)
$y - 1 = - \frac{2}{3} (x - 1)$
$\Rightarrow 2 x + 3 y = 5........ (4)$
Solving (1) and (4) we get $C (\frac{35}{2}, - 10)$
Solving (2) and (3) we get $A (- 13, \frac{- 33}{2})$
Equation of BC is $26 x - 122 y - 1675 = 0$

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