Answer:
7.8 in
Step-by-step explanation:
Given:-
- The dimension of rectangular prism:
(3 x 4 x 6) inches
Find:-
What is the length of the diagonal from the point R to point S, to the nearest tenth of an inch?
Solution:-
- We will set up an origin with coordinates ( 0 , 0 , 0 ) at point R. Then the coordinates of point S would be ( 3 , 4 , 6 ).
- Then we will use the distance between two points formula in cartesian coordinate system:
Distance = ![\sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2 + (z_1 - z_2)^2}](https://tex.z-dn.net/?f=%5Csqrt%7B%28x_1%20-%20x_2%29%5E2%20%2B%20%28y_1%20-%20y_2%29%5E2%20%2B%20%28z_1%20-%20z_2%29%5E2%7D)
Where the coordinates of two points ( x1 , y1 , z1 ) & ( x2 , y2 , z2 ).
- Using R( 0 , 0 , 0 ) & S( 3 , 4 , 6 ), the distance |RS| would be:
![|RS| = \sqrt{(0 - 3)^2 + (0 - 4)^2 + (0 - 6)^2}\\\\|RS| = \sqrt{ 9 + 16 + 36}\\\\|RS| = \sqrt{61} = 7.81024](https://tex.z-dn.net/?f=%7CRS%7C%20%3D%20%5Csqrt%7B%280%20-%203%29%5E2%20%2B%20%280%20-%204%29%5E2%20%2B%20%280%20-%206%29%5E2%7D%5C%5C%5C%5C%7CRS%7C%20%3D%20%5Csqrt%7B%209%20%2B%2016%20%2B%2036%7D%5C%5C%5C%5C%7CRS%7C%20%3D%20%5Csqrt%7B61%7D%20%3D%207.81024)
- The distance |RS| to nearest 10th of an inch is = 7.8 in