Question

To the nearest tenth, what is the distance between the points (1, –2, 5) and (0, 7, –4)?

Answer 1

Answer:

$\boxed{12.8}$

Step-by-step explanation:

The coordinates of your points, (1, –2, 5) and (0, 7, –4), are 3D  (x, y, z) coordinates. They represent the diagonal of a rectangular prism.

The length of the sides are

x₂ - x₁ = |0 – 1|     = 1

y₂ - y₁ = |7 – (-2)| = 9

z₂ - z₁ = |-4 – 5|   = 9

The prism has the dimensions 9 × 9 × 1 as shown in the diagram.

We can use the Pythagorean theorem to calculate the length of the diagonal, d

Look first at the red diagonal on the base of the prism.

x² = 9² + 9² = 81 + 81 = 162

Now, look at the main diagonal.

d² = x² + h² = 162 + 1² = 162 + 1 = 163

d = √163 =12.8

$\boxed{ \textbf{The distance between the two points is 12.8.}}$