The length of the perpendicular from the poin | vedclass

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(B) The given line is $\frac{x}{a} + \frac{y}{b} = 1$,which can be rewritten as $bx + ay - ab = 0$. The length of the perpendicular from a point $(x_{

Vedclass · Accepted Answer

$\left| \frac{ab}{\sqrt{a^{2} + b^{2}}} \right|$ units

Vedclass · Answer

(B) The given line is $\frac{x}{a} + \frac{y}{b} = 1$,which can be rewritten as $bx + ay - ab = 0$. The length of the perpendicular from a point $(x_{1}, y_{1})$ to the line $Ax + By + C = 0$ is given by $d = \left| \frac{Ax_{1} + By_{1} + C}{\sqrt{A^{2} + B^{2}}} \right|$. Substituting $A = b$,$B = a$,$C = -ab$,$x_{1} = a$,and $y_{1} = b$: $d = \left| \frac{b(a) + a(b) - ab}{\sqrt{b^{2} + a^{2}}} \right| = \left| \frac{ab + ab - ab}{\sqrt{a^{2} + b^{2}}} \right| = \left| \frac{ab}{\sqrt{a^{2} + b^{2}}} \right|$ units.

The length of the perpendicular from the point $P(a, b)$ to the line $\frac{x}{a} + \frac{y}{b} = 1$ is

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