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

Vedclass · Accepted Answer

$7$

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(B) The length of the perpendicular from a point $(x_1, y_1)$ to a line $Ax + By + C = 0$ is given by the formula: $d = \frac{|Ax_1 + By_1 + C|}{\sqrt{A^2 + B^2}}$.Given the point $(3, 1)$ and the line $4x + 3y + 20 = 0$,we have $A = 4$,$B = 3$,$C = 20$,$x_1 = 3$,and $y_1 = 1$.Substituting these values into the formula:$d = \frac{|4(3) + 3(1) + 20|}{\sqrt{4^2 + 3^2}}$$d = \frac{|12 + 3 + 20|}{\sqrt{16 + 9}}$$d = \frac{|35|}{\sqrt{25}}$$d = \frac{35}{5} = 7$.Thus,the length of the perpendicular is $7$.

The length of the perpendicular from the point $(3, 1)$ to the line $4x + 3y + 20 = 0$ is:

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