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(D) The formula for the length of the perpendicular from a point $(x_1, y_1, z_1)$ to the plane $Ax + By + Cz + D = 0$ is given by $d = \frac{|Ax_1 +

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$2\sqrt{6}$ units

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(D) The formula for the length of the perpendicular from a point $(x_1, y_1, z_1)$ to the plane $Ax + By + Cz + D = 0$ is given by $d = \frac{|Ax_1 + By_1 + Cz_1 + D|}{\sqrt{A^2 + B^2 + C^2}}$.Given point $P = (1, 1.5, 2)$ and plane $2x - 2y + 4z + 17 = 0$.Substituting the values into the formula:$d = \frac{|2(1) - 2(1.5) + 4(2) + 17|}{\sqrt{2^2 + (-2)^2 + 4^2}}$$d = \frac{|2 - 3 + 8 + 17|}{\sqrt{4 + 4 + 16}}$$d = \frac{|24|}{\sqrt{24}}$$d = \sqrt{24} = \sqrt{4 	imes 6} = 2\sqrt{6}$ units.Thus,the correct option is $D$.

The length of the foot of the perpendicular from the point $P\left(1, \frac{3}{2}, 2\right)$ to the plane $2x - 2y + 4z + 17 = 0$ is

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