The perpendicular distance of the straight li | vedclass

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Question

(A) The perpendicular distance $d$ of a line $Ax + By + C = 0$ from a point $(x_1, y_1)$ is given by the formula $d = \frac{|Ax_1 + By_1 + C|}{\sqrt{A

Vedclass · Accepted Answer

$\frac{7}{13}$

Vedclass · Answer

(A) The perpendicular distance $d$ of a line $Ax + By + C = 0$ from a point $(x_1, y_1)$ is given by the formula $d = \frac{|Ax_1 + By_1 + C|}{\sqrt{A^2 + B^2}}$.Given the line $12x + 5y - 7 = 0$ and the origin $(0, 0)$,we have $A = 12$,$B = 5$,$C = -7$,$x_1 = 0$,and $y_1 = 0$.Substituting these values into the formula:$d = \frac{|12(0) + 5(0) - 7|}{\sqrt{12^2 + 5^2}}$$d = \frac{|-7|}{\sqrt{144 + 25}}$$d = \frac{7}{\sqrt{169}}$$d = \frac{7}{13}$.

The perpendicular distance of the straight line $12x + 5y = 7$ from the origin is equal to

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