Question

Qual a distância do ponto A (1/3,2/3) e o ponto B (1/2,3/4). Desde já agradeço. --- (x/y = fração)

Answer 1

Boa noite!

Veja:

$A( \frac{1}{3},\; \frac{2}{3} )\;e\;B( \frac{1}{2} ,\; \frac{3}{4} )\\ \\ dAB= \sqrt{(XB-XA)^2\;+\;(YB-YA)^2} \\ \\ dAB= \sqrt{( \frac{1}{2} - \frac{1}{3})^2\;+\;( \frac{3}{4}- \frac{2}{3} )^2 } \\ \\ dAB= \sqrt{( \frac{1}{6})^2\;+\;( \frac{1}{12})^2 } \\ \\ dAB= \sqrt{ \frac{1}{36}\;+\; \frac{1}{144} } \\ \\ dAB= \sqrt{ \frac{5}{144} } \\ \\ dAB= \frac{ \sqrt{5} }{ \sqrt{144} } \\ \\ dAB= \frac{ \sqrt{5} }{12} \\ \\ Bons\; estudos!$

Answer 2

d= √(x2-x1)^2+(y2-y1)^2

d= √(1/2-1/3)^2+(3/4-2/3)^2

d= √(3-2/6)^2 + (9-8/12)^2

d= √(1/6)^2 +(1/12)^2

d= √1/36 + 1/144

36, 144 | 2
18, 72. | 2
9,36. |. 2
9, 18. | 2
9 , 9. |. 3
3,. 3. |. 3
1,. 1

m.m.c(36,144)= 2*2*2*2*3*3= 144

d= √4+1/144

d= √5/144

d= 1/12√5