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

2 Answers
Aug 29, 2016

Answer:

#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

Answer:

#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)#