First slide

Equation of line in Straight lines

Question

If algebraic sum of distances of a variable line from points (2, 0), (0, 2) and (– 2, – 2) is zero, then the line passes through the fixed point

Moderate

A

(– 1, – 1)
B

(0, 0)
C

(1, 1)
D

(2, 2)

Solution

Let the equation of the variable line be
$a x + b y + c = 0$
then according to the given condition
$\frac{2 a + c}{\sqrt{a^{2} + b^{2}}} + \frac{2 b + c}{\sqrt{a^{2} + b^{2}}} + \frac{- 2 a - 2 b + c}{\sqrt{a^{2} + b^{2}}} = 0$
$\Rightarrow c = 0$
which shows that the line passes through (0, 0) for all values of $a$ and $b$ .

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