The length of the perpendicular drawn from th | vedclass

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Question

(A) The given equation of the line is $\frac{x}{3} - \frac{y}{4} = 1$.Multiplying by $12$,we get $4x - 3y = 12$,which can be written as $4x - 3y - 12

Vedclass · Accepted Answer

$2\frac{2}{5}$

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(A) The given equation of the line is $\frac{x}{3} - \frac{y}{4} = 1$.Multiplying by $12$,we get $4x - 3y = 12$,which can be written as $4x - 3y - 12 = 0$.The formula for the perpendicular distance $d$ from a point $(x_1, y_1)$ to the line $Ax + By + C = 0$ is $d = \frac{|Ax_1 + By_1 + C|}{\sqrt{A^2 + B^2}}$.Here,$(x_1, y_1) = (0, 0)$,$A = 4$,$B = -3$,and $C = -12$.Substituting these values,$d = \frac{|4(0) - 3(0) - 12|}{\sqrt{4^2 + (-3)^2}} = \frac{|-12|}{\sqrt{16 + 9}} = \frac{12}{\sqrt{25}} = \frac{12}{5}$.Converting to a mixed fraction,$\frac{12}{5} = 2\frac{2}{5}$.

The length of the perpendicular drawn from the origin upon the straight line $\frac{x}{3} - \frac{y}{4} = 1$ is

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