Considera los puntos P(8, 5) y R(12, - 3) del plano coordenado?

1. P(8, 5) y R(12, - 3)Q₁(9, 3) r = <img src="https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B3%7D" />

Determinamos las ditancias PQ₁Q₁R

<img src="https://tex.z-dn.net/?f=%5Cleft%28x_1%2C%5C%3Ay_1%5Cright%29%2C%5C%3A%5Cleft%28x_2%2C%5C%3Ay_2%5Cright%29%3A%5Cquad%20%5Csqrt%7B%5Cleft%28x_2-x_1%5Cright%29%5E2%2B%5Cleft%28y_2-y_1%5Cright%29%5E2%7D" />

PQ₁

<img src="https://tex.z-dn.net/?f=%5Cleft%288%2C%5C%3A5%5Cright%29%5Cmathrm%7B%5C%3A%2C%5C%3A%7D%5Cleft%289%2C%5C%3A3%5Cright%29%3A%5Csqrt%7B%5Cleft%289-8%5Cright%29%5E2%2B%5Cleft%283-%205%5Cright%29%5E2%7D%3D%5Csqrt%7B5%7D" />

Q₁R

<img src="https://tex.z-dn.net/?f=%5Cleft%289%2C%5C%3A3%5Cright%29%5Cmathrm%7B%5C%3A%2C%5C%3A%7D%5Cleft%2812%2C%5C%3A-3%5Cright%29%3A%5Csqrt%7B%5Cleft%2812-9%5Cright%29%5E2%2B%5Cleft%28-3-3%5Cright%29%5E2%7D%3D3%5Csqrt%7B5%7D" />

Calculamos r :

<img src="https://tex.z-dn.net/?f=r%20%3D%20%20%5Cfrac%7BdPQ1%7D%7BdQ1R%7D%20%3D%20%20%5Cfrac%7B%5Csqrt%7B5%7D%7D%7B3%5Csqrt%7B5%7D%7D%3D%20%5Cfrac%7B1%7D%7B3%7D" />

Realizamos el mismo procedimiento para las demás :

2.

P(8, 5) y R(12, - 3)Q₂(10, 1) r = <img src="https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B1%7D" />

3.

P(8, 5) y R(12, - 3)Q₃(11, - 1) r = <img src="https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B1%7D" />.