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

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]