Use the rotation formulas (5) to show that distance is invariant under a rotation of axes That is, show that the distance from P 1 (x 1 , y 1 ) to P 2 (x 2 , y 2 ) in the xy plane equals the distance from P 1 (x ' 1 , y ' 1 ) to P 2 (x ' 2 , y ' 2 ) in x 'y ' plane ...

d y xx x sin 0 y cos 0 x sin 0 y cos x cos 0 y sin 0 x ...

Use the rotation formulas (5) to show that distance is invariant under a rotation of axes. That

Question:

Use the rotation formulas (5) to show that distance is invariant under a rotation of axes. That is, show that the distance from P₁ = (x₁, y₁) to P₂ = (x₂, y₂) in the xy-plane equals the distance from P₁ = (x'₁, y'₁) to P₂ = (x'₂, y'₂) in x'y'-plane.