Question
Find the length of the perpendicular from the point (4, -7) to the line joining the origin and the point of intersection of the lines 2x - 3y + 14 = 0 and 5x + 4y - 7 = 0.
✓
Answer
The point of intersection of the lines 2x - 3y + 14 = 0 and 5x + 4y - 7 = 0 can be found out by solving these equations.Solving these equations we get, $\text{x}=-\frac{35}{23}$ and $\text{y}=\frac{252}{69}$
Equation of line joining origin and the point $\Big(-\frac{35}{23},\frac{252}{69}\Big)$ is y = mx, where $\text{m}=\frac{\frac{252}{69}}{-\frac{35}{23}}=-\frac{12}{5}$
Therefore the equation of required line is $\text{y}=-\frac{12\text{x}}{5}$
$12\text{x}+5\text{y}=0$
Perpendicular distance from (4, -7) to 12x + 5y = 0 is
$\text{p}=\Bigg|\frac{12(4)+5(-7)}{\sqrt{12^2+(-5)^2}}\Bigg|=\frac{13}{13}=1$
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