Question

calcule a distância entre os pontos A (-2,m) e B (1,3)​

Answer 1

$A(-2,m)\\B(1,3)\\\\d_{AB} = \sqrt{\left(x_B-x_A\right)^2+(y_B-y_B)^2}\\d_{AB} = \sqrt{(1-(-2))^2+(3-m)^2}\\d_{AB} = \sqrt{(1+2)^2+(3^2-2\cdot 3 \cdot m+m^2)}\\d_{AB} = \sqrt{9+(9-6m+m^2)}$

Resolvendo a equação do segundo grau:

$m^2-6m+9=0\\\Delta = (-6)^2-4 \cdot 1 \cdot 9\\\Delta = 36-36\\\Delta = 0\\\\m = \dfrac{-(-6) \pm \sqrt{0}}{2 \cdot 1} = \dfrac{6}{2} = 3$

$\text{Assim:}\\\\d_{AB} = \sqrt{9+(9-6\cdot 3+3^2)}\\d_{AB} = \sqrt{9+(9-18+9)}\\d_{AB} = \sqrt{9 + 0}\\d_{AB} = \sqrt{9}\\\boxed{\boxed{d_{AB} = 3}}$