The distance from the point to the plane is 21. 7
How to determine the distance
From the information given, we have the following deductions;
The plane 9x - y - 4z = -52
The points ( 3, 2 , -2 ) are designated x ,y , z and x = 3 , y = 2, z = -2
The formula for a point to a plane is expressed as;
Distance = [tex]\frac{|Ax + Bx + Cx + Dx}{\sqrt{A^2 + B^2 + C^2} }[/tex]
Substitute the values
Distance = [tex]\frac{|9(3) + -1(2) + -4(-2) + (-52)|}{\sqrt{(3)^2 + (2)^2 + (-2)^2} }[/tex]
Distance = [tex]\frac{27 + 2 + 8 + 52}{\sqrt{17} }[/tex]
Distance = 21. 7
Thus, the distance from the point to the plane is 21. 7
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