Find the distance between the point $( 9,9,3 )$ and the plane $15 x - 3 y - 8 z = 10$ Round your answer to two decimal place.
A) $4.79$
B) $6.79$
C) $4.29$
D) $7.79$
E) $5.79$

Question

Quizplus · Accepted Answer

To find the distance between a point $(x_0,y_0,z_0)$ and a plane $Ax+By+Cz+D=0$, we use the formula: $$d=\frac{|Ax_0+By_0+Cz_0+D|}{\sqrt{A^2+B^2+C^2}}.$$
In this case, we have $x_0=9$, $y_0=9$, $z_0=3$, $A=15$, $B=-3$, $C=-8$, and $D=10$. Substituting these into the formula, we get:
$$d=\frac{|15(9)-3(9)-8(3)+10|}{\sqrt{15^2+(-3)^2+(-8)^2}}\approx 4.29.$$
Therefore, the answer is $\boxed{\textbf{(C)}}$.

Find the Distance Between the Point (9,9,3)( 9,9,3 )(9,9,3) And the Plane

Find the Distance Between the Point $( 9,9,3 )$ And the Plane