If the foot of the perpendicular drawn from t | vedclass

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Question

(A) Let the origin be $O(0, 0)$ and the foot of the perpendicular be $P(3, -4)$.The slope of the line segment $OP$ is $m_{OP} = \frac{-4 - 0}{3 - 0} =

Vedclass · Accepted Answer

$3x - 4y = 25$

Vedclass · Answer

(A) Let the origin be $O(0, 0)$ and the foot of the perpendicular be $P(3, -4)$.The slope of the line segment $OP$ is $m_{OP} = \frac{-4 - 0}{3 - 0} = -\frac{4}{3}$.Since the line is perpendicular to $OP$,the slope of the required line $m$ is the negative reciprocal of $m_{OP}$,so $m = -\frac{1}{m_{OP}} = \frac{3}{4}$.The required line passes through the point $P(3, -4)$ and has a slope $m = \frac{3}{4}$.Using the point-slope form $y - y_1 = m(x - x_1)$:$y - (-4) = \frac{3}{4}(x - 3)$$y + 4 = \frac{3}{4}(x - 3)$$4(y + 4) = 3(x - 3)$$4y + 16 = 3x - 9$$3x - 4y = 25$.

If the foot of the perpendicular drawn from the origin to a straight line is $(3, -4)$,then the equation of the line is:

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