Answer:
[tex]\boxed{12.8}\\[/tex]
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
[tex]\boxed{ \textbf{The distance between the two points is 12.8.}}\\[/tex]
