To find the shortest distance from a point to a plane, we can use the formula:
Distance = |ax + by + cz + d| / √(a^2 + b^2 + c^2)
Here, the equation of the plane is 2x + 4y + 2z = 8, which can be rewritten as 2x + 4y + 2z - 8 = 0.
Comparing this to the general form of the equation ax + by + cz + d = 0, we have:
a = 2, b = 4, c = 2, and d = -8.
Now, let's substitute the values of the point (1, 0, -2) into the formula:
Distance = |(2 * 1) + (4 * 0) + (2 * -2) - 8| / √((2^2) + (4^2) + (2^2))
Simplifying:
Distance = |2 - 4 - 4 - 8| / √(4 + 16 + 4)
Distance = |-14| / √24
Distance = 14 / √24
Distance ≈ 2.85 (rounded to two decimal places)
Therefore, the shortest distance from the point (1, 0, -2) to the plane 2x + 4y + 2z = 8 is approximately 2.85 units.