Urgente, ayuda con este problema de Algebra Lineal?

Datos

1) Punto fuera de la recta : <img src="https://tex.z-dn.net/?f=P%3D%28x_0%2Cy_0%29" />

2) Ecuación de la recta : <img src="https://tex.z-dn.net/?f=Ax%2BBy%2BC%3D0" />

Solución

Elijamos un punto cualquiera sobre la recta<img src="https://tex.z-dn.net/?f=Q%3D%28x_1%2Cy_1%29" />, esto es <img src="https://tex.z-dn.net/?f=Ax_1%2BBy_1%2BC%3D0" /> .

( * )

Nos serviremos del vector<img src="https://tex.z-dn.net/?f=%5Cvec%7Bv%7D%3DQ-P%3D%28x_1-x_0%2Cy_1-y_0%29" /> para proyectarlo sobre una recta perpendicular a la recta dada, cuyo vector direccional es<img src="https://tex.z-dn.net/?f=%5Cvec%20w%3D%28A%2CB%29" />

<img src="https://tex.z-dn.net/?f=%5Cvec%20l%3D%5Ctext%7Bproy%7D_%7B%5Cvec%20w%7D%5C%2C%20%5Cvec%20v%5C%5C%20%5C%5C%0A%5Cvec%20l%3D%5Cleft%28%5Cdfrac%7B%5Cvec%20v%5Ccdot%20%5Cvec%20w%7D%7B%7C%5Cvec%20w%7C%5E2%7D%5Cright%29%5Ccdot%20%5Cvec%20w%5C%5C%20%5C%5C%20%5C%5C%0A%5Cvec%20l%3D%5Cleft%28%5Cdfrac%7B%28x_1-x_0%2Cy_1-y_0%29%5Ccdot%28A%2CB%29%7D%7B%7C%28A%2CB%29%7C%5E2%7D%5Cright%29%5Ccdot%20%28A%2CB%29%5C%5C%20%5C%5C%20%5C%5C%0A%5Cvec%20l%3D%5Cdfrac%7BA%28x_1-x_0%29%2BB%28y_1-y_0%29%7D%7B%5Csqrt%7BA%5E2%2BB%5E2%7D%5E2%7D%5Ccdot%20%28A%2CB%29" />

<img src="https://tex.z-dn.net/?f=%5Cvec%20l%3D%5Cdfrac%7B%28Ax_1%2BBy_1%29-Ax_0-By_0%7D%7B%5Csqrt%7BA%5E2%2BB%5E2%7D%5E2%7D%5Ccdot%20%28A%2CB%29%5C%5C%20%5C%5C%20%5C%5C%0A%5Cboxed%7B%5Cvec%20l%3D%5Cdfrac%7B-C-Ax_0-By_0%7D%7B%5Csqrt%7BA%5E2%2BB%5E2%7D%5E2%7D%5Ccdot%20%28A%2CB%29%7D%0A" />

Ahora solo necesitamos la medida del vector<img src="https://tex.z-dn.net/?f=%5Cvec%20l" />

<img src="https://tex.z-dn.net/?f=%5Cleft%7C%5C%2C%5Cvec%20l%5C%2C%5Cright%7C%3D%5Cleft%7C%5Cdfrac%7B-C-Ax_0-By_0%7D%7B%5Csqrt%7BA%5E2%2BB%5E2%7D%5E2%7D%5Ccdot%20%28A%2CB%29%5Cright%7C%5C%5C%20%5C%5C%20%5C%5C%0A%5Cleft%7C%5C%2C%5Cvec%20l%5C%2C%5Cright%7C%3D%5Cleft%7C%5Cdfrac%7B-C-Ax_0-By_0%7D%7B%5Csqrt%7BA%5E2%2BB%5E2%7D%5E2%7D%5Cright%7C%5Ccdot%20%5Cleft%7C%28A%2CB%29%5Cright%7C%5C%5C%20%5C%5C%20%5C%5C%0A%5Cleft%7C%5C%2C%5Cvec%20l%5C%2C%5Cright%7C%3D%5Cdfrac%7B%5Cleft%7CAx_0%2BBy_0%2BC%5Cright%7C%7D%7B%5Csqrt%7BA%5E2%2BB%5E2%7D%5E2%7D%5Ccdot%20%5Csqrt%7BA%5E2%2BB%5E2%7D%5C%5C%20%5C%5C%20%5C%5C%20%5C%5C%0A%5Cboxed%7B%5Cboxed%7B%5Cleft%7C%5C%2C%5Cvec%20l%5C%2C%5Cright%7C%3D%5Cdfrac%7B%5Cleft%7CAx_0%2BBy_0%2BC%5Cright%7C%7D%7B%5Csqrt%7BA%5E2%2BB%5E2%7D%7D%7D%7D" />.