What is the distance between the points (-3, 1, 2) and (4, 3, -2) to the nearest tenth?

To find the distance between the points ((-3, 1, 2)) and ((4, 3, -2)) in a three-dimensional space, we use the distance formula for 3D points, which is given by:

[

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

]

Here, ((x_1, y_1, z_1) = (-3, 1, 2)) and ((x_2, y_2, z_2) = (4, 3, -2)).

1. Calculate the differences in each coordinate:

• (x_2 - x_1 = 4 - (-3) = 4 + 3 = 7)

• (y_2 - y_1 = 3 - 1 = 2)

• (z_2 - z_1 = -2 - 2 = -4)

2. Now substitute these values into the distance formula:

[

d = \sqrt{(7)^2 + (