Question

20) Determine o ponto p, pertencente ao eixo das abscissas sabendo que é esquidistante dos pontos A(2-1) e B(3-5).​

Answer 1

Dados:

$A(x_A,y_A)=A(2,-1)\\ B(x_B,y_B)=B(3,-5)\\ P(x_P,y_P)=P(x_P,0)\ \to\ d_{AP}=d_{BP}$

$d^2_{AP}=d^2_{BP}\ \therefore\ (x_P-x_A)^2+(y_P-y_A)^2=(x_P-x_B)^2+(y_P-y_B)^2\ \therefore$

$(x_P-2)^2+(0+1)^2=(x_P-3)^2+(0+5)^2\ \therefore$

$x_P^2-4x_P+4+1=x_P^2-6x_P+9+25\ \therefore$

$-4x_P+5=-6x_P+34\ \therefore\ 2x_P=29\ \therefore\ \boxed{x_P=\dfrac{29}{2}}$

$\boxed{P\bigg(\dfrac{29}{2},0\bigg)}$