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(D) The perpendicular distance $d$ from a point $(x_1, y_1)$ to the line $ax + by + c = 0$ is given by the formula: $d = \left| \frac{ax_1 + by_1 + c}

Vedclass · Accepted Answer

$28, -42$

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(D) The perpendicular distance $d$ from a point $(x_1, y_1)$ to the line $ax + by + c = 0$ is given by the formula: $d = \left| \frac{ax_1 + by_1 + c}{\sqrt{a^2 + b^2}} \right|$.Given the point $(1, 1)$,the line $3x + 4y + c = 0$,and the distance $d = 7$:$7 = \left| \frac{3(1) + 4(1) + c}{\sqrt{3^2 + 4^2}} \right|$$7 = \left| \frac{7 + c}{\sqrt{9 + 16}} \right|$$7 = \left| \frac{7 + c}{5} \right|$$|7 + c| = 35$This implies $7 + c = 35$ or $7 + c = -35$.If $7 + c = 35$,then $c = 28$.If $7 + c = -35$,then $c = -42$.Thus,the possible values of $c$ are $28$ and $-42$.

If the perpendicular distance from the point $(1, 1)$ to the line $3x + 4y + c = 0$ is $7$,then the possible values of $c$ are:

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