What is the distance between (9, 2, 0) and (0, 6, 0) ?

2 Answers
Aug 29, 2016

sqrt97≈9.849

Explanation:

Use the color(blue)"3-d version of the distance formula"

color(red)(|bar(ul(color(white)(a/a)color(black)(d=sqrt((x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2))color(white)(a/a)|)))
where (x_1,y_1,z_1)" and " (x_2,y_2,z_2)" are 2 coordinate points"

here the 2 points are (9 ,2 ,0) and (0 ,6 ,0)

let (x_1,y_1,z_1)=(9,2,0)" and " (x_2,y_2,z_2)=(0,6,0)

d=sqrt((0-9)^2+(6-2)^2+0^2)=sqrt(81+16)=sqrt97≈9.849

Aug 29, 2016

sqrt(97)

Explanation:

The (Euclidean) distance between (x_1, y_1, z_1) and (x_2, y_2, z_2) is given by the distance formula:

d = sqrt((x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2

In our example, (x_1, y_1, z_1) = (9, 2, 0), (x_2, y_2, z_2) = (0, 6, 0) and we find:

d = sqrt((0-9)^2+(6-2)^2+(0-0)^2) = sqrt(81+16+0) = sqrt(97)