Question

Um ponto P pertence ao eixo das abscissas (x) equidista de A(1, -1) e B(2, 3). Obtenha as coordenadas de P.

Answer 1

O ponto P(x,y) pertence ao eixo das abscissas, então y = 0, ou seja, P(x,0).

Ponto P equidistante de A(1, -1) e B(2, 3) :

$\displaystyle \sqrt{(\text x_{\text P}-\text x_\text A)^2+(\text y_\text P-\text y_\text A)^2}=\sqrt{(\text x_\text P-\text x_\text B)^2+(\text y_\text p-\text y_\text B)^2}\\\\ \sqrt{(\text x-1)^2+(0-(-1))^2}=\sqrt{(\text x-2)^2+(0-3)^2} \\\\ \sqrt{(\text x-1)^2+1}=\sqrt{(\text x-2)^2+9} \\\\ (\text x-1)^2+1=(\text x-2)^2+9 \\\\ \text x^2-2\text x+1+1=\text x^2-4\text x+4+9 \\\\ 2\text x= 11 \\\\ \text x= \frac{11}{2} \\\\ \underline{\text{Portanto o ponto P {\'e}}} :$

$\huge\boxed{\text P(\ \frac{11}{2},\ 0\ )\ }\checkmark$