Ponto Q tem sua ordenada igual ao dobro da sua abscissa, isto é :
[tex]{\text Q \to \text y = 2\text x}[/tex]
ponto Q ( x , y ).
E é equidistante dos pontos D(-4,3) e B(2,1). Fazendo distância entre dois pontos :
[tex]\sqrt{(\text x-(-4))^2+(\text y-3)^2}=\sqrt{(\text x-2)^2+(\text y-1)^2}\\\\ \sqrt{(\text x+4)^2+(\text y-3)^2}=\sqrt{(\text x-2)^2+(\text y-1)^2} \\\\ (\text x+4)^2+(\text y-3)^2=(\text x-2)^2+(\text y-1)^2\\\\ \underline{\text{Aplicando a propriedade do ponto Q : y = 2x}} \\\\ (\text x+4)^2+(2\text x-3)^2=(\text x-2)^2+(2\text x-1)^2 \\\\ \text x^2+8\text x+16+4\text x^2-12\text x+9=\text x^2-4\text x+4+4\text x^2-4\text x+1 \\\\ 5\text x^2 -4\text x+25=5\text x^2-8\text x+5 \\\\ -4\text x+25=-8\text x+5[/tex]
[tex]8\text x-4\text x=5-25 \\\\ 4\text x = -20 \\\\ \text x = -5} \\\\ \text{Sabendo que y = 2x, logo } : \\\\ \text y = 2.(-5) \to \text y = -10 \\\\ \underline{\text{Portanto o ponto Q {\'e}}}: \\\\ \huge\boxed{ \text {Q = ( -5 , -10 )}\ }\checkmark[/tex]
