First slide

Equation of line in Straight lines

Question

The perpendicular distance from $(1, 3)$ to the line passing through the point $P (2, 1)$ where the point $P (2, 1)$ bisects the portion of the line intercepted between the axes.

Moderate

A

$\frac{15}{4}$
B

$\frac{4}{5}$
C

$\frac{3}{5}$
D

$\frac{3 \sqrt{5}}{5}$

Solution

$The equation of the line whose portion intercepted between the axes bisected by (x_{1}, y_{1}) is \frac{x}{x_{1}} + \frac{y}{y_{1}} = 2$
$Hence the equation of the line whose portion intercepted between the axes at P (2, 1) is \frac{x}{2} + y = 2$
$Rewrite the equation as x + 2 y - 4 = 0$
$The perpendicular distance from a point P (x_{1}, y_{1}) to the line a x + b y + c = 0 is |\frac{a x_{1} + b y_{1} + c}{\sqrt{a^{2} + b^{2}}}|$
$The perpendicular distance from a point (1, 3) to the line x + 2 y - 4 = 0 is$
$|\frac{1 + 2 (3) - 4}{\sqrt{1 + 4}}| = \frac{3}{\sqrt{5}} = \frac{3 \sqrt{5}}{5}$

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