Question

determine a distancia entre os pontos a seguir :
a) A(2,5) e B(-3,1)
b) P(-4,0) e Q (1,-5)
c R(-1\2, 1) e S(5,-1)

Answer 1

Oi Lais  :)
Nesse caso podemos utilizar esse modo:
$dAB= \sqrt{(xb-xa)^2+(yb-ya)^2}$

onde :   A ( xa, ya)  e B ( xb, yb)


a)
$dAB= \sqrt{(-3-2)^2+(1-5)^2} \\ \\ dAB= \sqrt{(-5)^2+(-4)^2} \\ \\ dAB= \sqrt{25+16} \\ \\ dAB= \sqrt{41}$

b)
$dPQ= \sqrt{(1-(-4))^2+(-5-0)^2} \\ \\ dAB= \sqrt{(5)^2+(-5)^2} \\ \\ dAB= \sqrt{25+25} \\ \\ dAB= \sqrt{50} \\ \\ dAB= 5\sqrt{2}$

c)
$dRS= \sqrt{(5-( -\frac{1}{2} ))^2+(-1-1)^2} \\ \\ dRS= \sqrt{(5+\frac{1}{2})^2+(-2)^2} \\ \\ dRS= \sqrt{(\frac{11}{2})^2+(-2)^2} \\ \\ dRS= \sqrt{\frac{121}{4}+4} \\ \\ dRS= \sqrt{\frac{121+16}{4}} \\ \\ dRS= \sqrt{\frac{137}{4}} \\ \\ dRS=\frac{ \sqrt{137}}{ \sqrt{4} } \\ \\ dRS=\frac{ \sqrt{137}}{ 2 }$