Distance from point to plane example

Example

Find the distance from the point P = (4, - 4, 3) to the plane 2x - 2y + 5z + 8 = 0. (This is pictured in the distance to plane CVT in its original view, which you can restore by pressing Home).

Solution: We use formula (2) from the distance to plane reading. From the equation for the plane we substitute A = 2, B = - 2, C = 5, D = 8. From the point P, we substitute x₁ = 4, y₁ = - 4, and z₁ = 3. The distance from P to the plane is

$${\frac{{\vert 2 \cdot 4 + (-2)\cdot(-4) + 5 \cdot 3 + 8 \vert}}{{\sqrt{2^2+(-2)^2 + 5^2}}}} {\frac{{39}}{{\sqrt{33}}}} \approx$$