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(D) The perpendicular distance $d$ of a line $Ax + By + C = 0$ from the origin $(0, 0)$ is given by $d = \frac{|C|}{\sqrt{A^2 + B^2}}$.For option $A$:

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$5x - 2y - 3 = 0$

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(D) The perpendicular distance $d$ of a line $Ax + By + C = 0$ from the origin $(0, 0)$ is given by $d = \frac{|C|}{\sqrt{A^2 + B^2}}$.For option $A$: $d_A = \frac{|4|}{\sqrt{3^2 + (-4)^2}} = \frac{4}{5} = 0.8$.For option $B$: $d_B = \frac{|-5|}{\sqrt{2^2 + (-3)^2}} = \frac{5}{\sqrt{13}} \approx \frac{5}{3.6} \approx 1.38$.For option $C$: $d_C = \frac{|12|}{\sqrt{4^2 + (-3)^2}} = \frac{12}{5} = 2.4$.For option $D$: $d_D = \frac{|-3|}{\sqrt{5^2 + (-2)^2}} = \frac{3}{\sqrt{29}} \approx \frac{3}{5.38} \approx 0.55$.Comparing the distances,$0.55 < 0.8 < 1.38 < 2.4$. Thus,the line in option $D$ is nearest to the origin.

From the following options,the line nearest to the origin is ....

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