Find the equation of the straight line passing through the origin and perpendicular to the line segment PQ…

Question

Find the equation of the straight line passing through the origin and perpendicular to the line segment PQ, where P is (0, 4) and Q is (−4, 0).

ScanSolve AI Tutor · Accepted Answer

Okay, Chimuka, let's tackle this geometry problem.

Identify the coordinates of points P and Q.
P is $(0, 4)$ .
Q is $(-4, 0)$ .
Calculate the slope of line PQ.
The slope $m$ of a line passing through two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by $m = \frac{y_2 - y_1}{x_2 - x_1}$ .
Using P $(0, 4)$ and Q $(-4, 0)$ :
$m_{PQ} = \frac{0 - 4}{-4 - 0} = \frac{-4}{-4} = 1$
Determine the slope of the line perpendicular to PQ.
If two lines are perpendicular, the product of their slopes is $-1$ . Let the slope of the required line be $m_{perp}$ .
$m_{perp} \cdot m_{PQ} = -1$ $m_{perp} \cdot 1 = -1$ $m_{perp} = -1$
Find the equation of the straight line.
The required line passes through the origin O $(0, 0)$ and has a slope $m_{perp} = -1$ .
Using the point-slope form $y - y_1 = m(x - x_1)$ :
$y - 0 = -1(x - 0)$ $y = -x$

Find the equation of the straight line passing through the origin and perpendicular to the line segment PQ, where P is (0, 4) and Q is (-4, 0).