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

The distance between a point and a plane is given by the formula $\frac{|ax+by+cz+d|}{\sqrt{a^2+b^2+c^2}}$, where $(x,y,z)$ is the point and $ax+by+cz+d=0$ is the equation of the plane.

In this case, the equation of the plane is $15x-3y-8z=10$, so $a=15$, $b=-3$, $c=-8$, and $d=-10$. Plugging in the values for the point $(9,9,3)$, we get:

$$\frac{|15(9)-3(9)-8(3)-10|}{\sqrt{15^2+(-3)^2+(-8)^2}}=\frac{|108|}{\sqrt{338}}\approx 4.29$$

Rounding to two decimal places, our answer is $\boxed{	extbf{(C) }4.29}$.

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