First slide

Equation of line in Straight lines

Question

If the foot of the perpendicular from the origin to straight line is at the point $(3, - 4) .$ Then the equation of the line is

Moderate

A

$3 x - 4 y = 25$
B

$3 x - 4 y + 25 = 0$
C

$4 x + 3 y - 25 = 0$
D

$4 x - 3 y + 25 = 0$

Solution

Let $O (0, 0)$ be the origin and $P (3, - 4)$ be the given point.
Slope of $O P = - \frac{4}{3}$
Slope of the required line $= \frac{3}{4}$
Clearly, required line passes through $P (3, - 4)$ and is perpendicular to $O P .$ So, its equation is
$y + 4 = \frac{3}{4} (x - 3)$ or, $3 x - 4 y - 25 = 0$
The equation of a line passing through two points $(x_{1}, y_{1})$ and $(x_{2}, Y_{2}),$ is
$y - y_{1} = (\frac{y_{2} - y_{1}}{x_{2} - x_{1}}) (x - x_{1})$

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